add colors
This commit is contained in:
parent
c12067684a
commit
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9
Makefile
9
Makefile
@ -13,7 +13,7 @@ BIBER = biber
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LATEX_OPTS := -output-directory=$(OUT_DIR) -interaction=nonstopmode -shell-escape
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.PHONY: default release clean
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.PHONY: default release clean scripts
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default: english
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release: german english
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@ -28,6 +28,13 @@ german:
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-cd $(SRC_DIR) && latexmk -lualatex -g main.tex
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mv $(OUT_DIR)/$(MAIN_PDF) $(OUT_DIR)/$(shell date -I)_de_Formelsammlung.pdf
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SCRIPT_DIR = scripts
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PY_SCRIPTS = $(wildcard $(SCRIPT_DIR)/*.py)
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PY_SCRIPTS_REL = $(notdir $(PY_SCRIPTS))
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scripts:
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-#cd $(SCRIPT_DIR) && for file in $(find -type f -name '*.py'); do echo "Running $$file"; python3 "$$file"; done
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cd $(SCRIPT_DIR) && $(foreach script,$(PY_SCRIPTS_REL),echo "Running $(script)"; python3 $(script);)
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# Clean auxiliary and output files
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clean:
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rm -r $(OUT_DIR)
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@ -44,6 +44,8 @@ The `<partname>:...:<lowest section name>` will be defined as `\fqname` (fully q
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- figure: `fig`
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- parts, (sub)sections: `sec`
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Use `misc` as (sub(sub))section for anything that can not be categorized within its (sub)section/part.
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### Files and directories
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Separate parts in different source files named `<partname>.tex`.
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If a part should be split up in multiple source files itself, use a
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47
scripts/ch_elchem.py
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47
scripts/ch_elchem.py
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@ -0,0 +1,47 @@
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#!/usr/bin env python3
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from formulasheet import *
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from scipy.constants import gas_constant, Avogadro, elementary_charge
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Faraday = Avogadro * elementary_charge
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@np.vectorize
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def fbutler_volmer_left(ac, z, eta, T):
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return np.exp((1-ac)*z*Faraday*eta/(gas_constant*T))
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@np.vectorize
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def fbutler_volmer_right(ac, z, eta, T):
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return -np.exp(-ac*z*Faraday*eta/(gas_constant*T))
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def fbutler_volmer(ac, z, eta, T):
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return fbutler_volmer_left(ac, z, eta, T) + fbutler_volmer_right(ac, z, eta, T)
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def butler_volmer():
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fig, ax = plt.subplots(figsize=size_half_third)
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ax.set_xlabel("$\\eta$")
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ax.set_ylabel("$i/i_0$")
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etas = np.linspace(-0.1, 0.1, 400)
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T = 300
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z = 1.0
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# other a
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alpha2, alpha3 = 0.2, 0.8
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i2 = fbutler_volmer(0.2, z, etas, T)
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i3 = fbutler_volmer(0.8, z, etas, T)
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ax.plot(etas, i2, color="blue", linestyle="dashed", label=f"$\\alpha={alpha2}$")
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ax.plot(etas, i3, color="green", linestyle="dashed", label=f"$\\alpha={alpha3}$")
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# 0.5
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ac = 0.5
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irel_left = fbutler_volmer_left(ac, z, etas, T)
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irel_right = fbutler_volmer_right(ac, z, etas, T)
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ax.plot(etas, irel_left, color="gray")
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ax.plot(etas, irel_right, color="gray")
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ax.plot(etas, irel_right + irel_left, color="black", label=f"$\\alpha=0.5$")
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ax.grid()
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ax.legend()
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ylim = 6
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ax.set_ylim(-ylim, ylim)
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return fig
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if __name__ == '__main__':
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export(butler_volmer(), "ch_butler_volmer")
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64
scripts/cm_phonons.py
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64
scripts/cm_phonons.py
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@ -0,0 +1,64 @@
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#!/usr/bin env python3
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from formulasheet import *
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def fone_atom_basis(q, a, M, C1, C2):
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return np.sqrt(4*C1/M * (np.sin(q*a/2)**2 + C2/C1 * np.sin(q*a)**2))
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def one_atom_basis():
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a = 1.
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C1 = 0.25
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C2 = 0
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M = 1.
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qs = np.linspace(-2*np.pi/a, 2*np.pi/a, 300)
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omega = fone_atom_basis(qs, a, M, C1, C2)
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fig, ax = plt.subplots(figsize=size_half_third)
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ax.set_xlabel(r"$q$")
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ax.set_xticks([i * np.pi/a for i in range(-2, 3)])
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ax.set_xticklabels([f"${i}\\pi/a$" if i != 0 else "0" for i in range(-2, 3)])
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ax.set_ylabel(r"$\omega$ in $\left[4C_1/M\right]$")
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yunit = np.sqrt(4*C1/M)
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ax.set_ylim(0, yunit+0.1)
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ax.set_yticks([0,yunit])
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ax.set_yticklabels(["0","1"])
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ax.plot(qs, omega)
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ax.text(-1.8*np.pi/a, 0.8, "NN\n$C_2=0$", ha='center')
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ax.text(0, 0.8, "1. BZ", ha='center')
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ax.vlines([-np.pi/a, np.pi/a], ymin=-2, ymax=2, color="black")
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ax.grid()
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return fig
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def ftwo_atom_basis_acoustic(q, a, M1, M2, C):
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return np.sqrt(C*(1/M1+1/M2) - C * np.sqrt((1/M1+1/M2)**2 - 4/(M1*M2) * np.sin(q*a/2)**2))
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def ftwo_atom_basis_optical(q, a, M1, M2, C):
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return np.sqrt(C*(1/M1+1/M2) + C * np.sqrt((1/M1+1/M2)**2 - 4/(M1*M2) * np.sin(q*a/2)**2))
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def two_atom_basis():
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a = 1.
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C = 0.25
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M1 = 1.
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M2 = 0.7
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qs = np.linspace(-2*np.pi/a, 2*np.pi/a, 300)
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omega_a = ftwo_atom_basis_acoustic(qs, a, M1, M2, C)
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omega_o = ftwo_atom_basis_optical(qs, a, M1, M2, C)
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fig, ax = plt.subplots(figsize=size_half_third)
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ax.plot(qs, omega_a, label="acoustic")
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ax.plot(qs, omega_o, label="optical")
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ax.text(0, 0.8, "1. BZ", ha='center')
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ax.vlines([-np.pi/a, np.pi/a], ymin=-2, ymax=2, color="black")
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ax.set_ylim(-0.03, 1.03)
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ax.set_ylabel(r"$\omega$ in $\left[\sqrt{2C\mu^{-1}}\right]$")
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yunit = np.sqrt(2*C*(1/M1+1/M2))
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ax.set_ylim(0, yunit+0.1)
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ax.set_yticks([0,yunit])
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ax.set_yticklabels(["0","1"])
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ax.set_xlabel(r"$q$")
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ax.set_xticks([i * np.pi/a for i in range(-2, 3)])
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ax.set_xticklabels([f"${i}\\pi/a$" if i != 0 else "0" for i in range(-2, 3)])
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ax.legend()
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ax.grid()
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return fig
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if __name__ == '__main__':
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export(one_atom_basis(), "cm_phonon_dispersion_one_atom_basis")
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export(two_atom_basis(), "cm_phonon_dispersion_two_atom_basis")
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File diff suppressed because one or more lines are too long
File diff suppressed because one or more lines are too long
@ -1,5 +1,6 @@
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from numpy import fmax
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from plot import *
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from formulasheet import *
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import itertools
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def get_fig():
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@ -22,7 +23,6 @@ def gauss():
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ax.plot(x, y, label=label)
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ax.legend()
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return fig
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export(gauss(), "distribution_gauss")
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# CAUCHY / LORENTZ
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def fcauchy(x, x_0, gamma):
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@ -37,7 +37,6 @@ def cauchy():
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ax.plot(x, y, label=label)
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ax.legend()
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return fig
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export(cauchy(), "distribution_cauchy")
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# MAXWELL-BOLTZMANN
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def fmaxwell(x, a):
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@ -53,7 +52,37 @@ def maxwell():
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ax.legend()
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return fig
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export(maxwell(), "distribution_maxwell-boltzmann")
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# GAMMA
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@np.vectorize
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def fgamma(x, alpha, lam):
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return lam**alpha / scp.special.gamma(alpha) * x**(alpha-1) * np.exp(-lam*x)
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def gamma():
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fig, ax = get_fig()
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x = np.linspace(0, 20, 300)
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for (alpha, lam) in itertools.product([1, 2, 5], [1, 2]):
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y = fgamma(x, alpha, lam)
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label = f"$\\alpha = {alpha}, \\lambda = {lam}$"
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ax.plot(x, y, label=label)
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ax.set_ylim(0, 1.1)
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ax.set_xlim(0, 10)
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ax.legend()
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return fig
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# BETA
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@np.vectorize
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def fbeta(x, alpha, beta):
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return x**(alpha-1) * (1-x)**(beta-1) / scp.special.beta(alpha, beta)
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def beta():
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fig, ax = get_fig()
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x = np.linspace(0, 20, 300)
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for (alpha, lam) in itertools.product([1, 2, 5], [1, 2]):
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y = fgamma(x, alpha, lam)
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label = f"$\\alpha = {alpha}, \\beta = {lam}$"
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ax.plot(x, y, label=label)
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ax.set_ylim(0, 1.1)
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ax.set_xlim(0, 10)
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ax.legend()
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return fig
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# POISSON
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@ -73,8 +102,6 @@ def poisson():
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ax.legend()
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return fig
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export(poisson(), "distribution_poisson")
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# BINOMIAL
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def binom(n, k):
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return scp.special.factorial(n) / (
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@ -98,9 +125,17 @@ def binomial():
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ax.legend()
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return fig
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export(binomial(), "distribution_binomial")
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if __name__ == '__main__':
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export(gauss(), "distribution_gauss")
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export(cauchy(), "distribution_cauchy")
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export(maxwell(), "distribution_maxwell-boltzmann")
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export(gamma(), "distribution_gamma")
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export(beta(), "distribution_beta")
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export(poisson(), "distribution_poisson")
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export(binomial(), "distribution_binomial")
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# FERMI-DIRAC
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# BOSE-EINSTEIN
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# see stat-mech
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71
scripts/formulasheet.py
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71
scripts/formulasheet.py
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@ -0,0 +1,71 @@
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#!/usr/bin env python3
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import os
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import matplotlib.pyplot as plt
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import numpy as np
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import math
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import scipy as scp
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if __name__ == "__main__": # make relative imports work as described here: https://peps.python.org/pep-0366/#proposed-change
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if __package__ is None:
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__package__ = "formulasheet"
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import sys
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filepath = os.path.realpath(os.path.abspath(__file__))
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sys.path.insert(0, os.path.dirname(os.path.dirname(filepath)))
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from util.mpl_colorscheme import set_mpl_colorscheme
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import util.colorschemes as cs
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# SET THE COLORSCHEME
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# hard white and black
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# cs.p_gruvbox["fg0"] = "#000000"
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# cs.p_gruvbox["bg0"] = "#ffffff"
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COLORSCHEME = cs.gruvbox_dark()
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# print(COLORSCHEME)
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# COLORSCHEME = cs.GRUVBOX_DARK
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tex_src_path = "../src/"
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img_out_dir = os.path.join(tex_src_path, "img")
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filetype = ".pdf"
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skipasserts = False
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full = 8
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size_half_half = (full/2, full/2)
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size_third_half = (full/3, full/2)
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size_half_third = (full/2, full/3)
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def assert_directory():
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if not skipasserts:
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assert os.path.abspath(".").endswith("scripts"), "Please run from the `scripts` directory"
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def texvar(var, val, math=True):
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s = "$" if math else ""
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s += f"\\{var} = {val}"
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if math: s += "$"
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return s
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def export(fig, name, notightlayout=False):
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assert_directory()
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filename = os.path.join(img_out_dir, name + filetype)
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if not notightlayout:
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fig.tight_layout()
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fig.savefig(filename) #, bbox_inches="tight")
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@np.vectorize
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def smooth_step(x: float, left_edge: float, right_edge: float):
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x = (x - left_edge) / (right_edge - left_edge)
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if x <= 0: return 0.
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elif x >= 1: return 1.
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else: return 3*(x*2) - 2*(x**3)
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# run even when imported
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set_mpl_colorscheme(COLORSCHEME)
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if __name__ == "__main__":
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assert_directory()
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s = \
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"""% This file was generated by scripts/formulasheet.py\n% Do not edit it directly, changes will be overwritten\n""" + cs.generate_latex_colorscheme(COLORSCHEME)
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filename = os.path.join(tex_src_path, "util/colorscheme.tex")
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print(f"Writing tex colorscheme to {filename}")
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with open(filename, "w") as file:
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file.write(s)
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149
scripts/mpl_colorscheme.py
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149
scripts/mpl_colorscheme.py
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"""
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Set the colorscheme for matplotlib plots and latex.
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Calling this script generates util/colorscheme.tex containing xcolor definitions.
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"""
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import matplotlib as mpl
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import matplotlib.pyplot as plt
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from cycler import cycler
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skipasserts = False
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GRUVBOX = {
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"bg0": "#282828",
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"bg0-hard": "#1d2021",
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"bg0-soft": "#32302f",
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"bg1": "#3c3836",
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"bg2": "#504945",
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"bg3": "#665c54",
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"bg4": "#7c6f64",
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"fg0": "#fbf1c7",
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"fg0-hard": "#f9f5d7",
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"fg0-soft": "#f2e5bc",
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"fg1": "#ebdbb2",
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"fg2": "#d5c4a1",
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"fg3": "#bdae93",
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"fg4": "#a89984",
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"dark-red": "#cc241d",
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"dark-green": "#98971a",
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"dark-yellow": "#d79921",
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"dark-blue": "#458588",
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"dark-purple": "#b16286",
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"dark-aqua": "#689d6a",
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"dark-orange": "#d65d0e",
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"dark-gray": "#928374",
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"light-red": "#fb4934",
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"light-green": "#b8bb26",
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"light-yellow": "#fabd2f",
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"light-blue": "#83a598",
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"light-purple": "#d3869b",
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"light-aqua": "#8ec07c",
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"light-orange": "#f38019",
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"light-gray": "#a89984",
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"alt-red": "#9d0006",
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"alt-green": "#79740e",
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"alt-yellow": "#b57614",
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"alt-blue": "#076678",
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"alt-purple": "#8f3f71",
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"alt-aqua": "#427b58",
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"alt-orange": "#af3a03",
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"alt-gray": "#7c6f64",
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}
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FORMULASHEET_COLORSCHEME = GRUVBOX
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colors = ["red", "orange", "yellow", "green", "aqua", "blue", "purple", "gray"]
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# default order for matplotlib
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color_order = ["blue", "orange", "green", "red", "purple", "yellow", "aqua", "gray"]
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def set_mpl_colorscheme(palette: dict[str, str], variant="dark"):
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P = palette
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if variant == "dark":
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FIG_BG_COLOR = P["bg0"]
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PLT_FG_COLOR = P["fg0"]
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PLT_BG_COLOR = P["bg0"]
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PLT_GRID_COLOR = P["bg2"]
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LEGEND_FG_COLOR = PLT_FG_COLOR
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LEGEND_BG_COLOR = P["bg1"]
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LEGEND_BORDER_COLOR = P["bg2"]
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else:
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FIG_BG_COLOR = P["fg0"]
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PLT_FG_COLOR = P["bg0"]
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PLT_BG_COLOR = P["fg0"]
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PLT_GRID_COLOR = P["fg2"]
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LEGEND_FG_COLOR = PLT_FG_COLOR
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LEGEND_BG_COLOR = P["fg1"]
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LEGEND_BORDER_COLOR = P["fg2"]
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COLORS = [P[f"{variant}-{c}"] for c in color_order]
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color_rcParams = {
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'axes.edgecolor': PLT_FG_COLOR,
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'axes.facecolor': PLT_BG_COLOR,
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'axes.labelcolor': PLT_FG_COLOR,
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'axes.titlecolor': 'auto',
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# 'axes.prop_cycle': cycler('color', ['#1f77b4', '#ff7f0e', '#2ca02c', '#d62728', '#9467bd', '#8c564b', '#e377c2', '#7f7f7f', '#bcbd22', '#17becf']),
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'axes.prop_cycle': cycler('color', COLORS),
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# 'axes3d.xaxis.panecolor': (0.95, 0.95, 0.95, 0.5),
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# 'axes3d.yaxis.panecolor': (0.9, 0.9, 0.9, 0.5),
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# 'axes3d.zaxis.panecolor': (0.925, 0.925, 0.925, 0.5),
|
||||
# 'boxplot.boxprops.color': 'black',
|
||||
# 'boxplot.capprops.color': 'black',
|
||||
# 'boxplot.flierprops.color': 'black',
|
||||
# 'boxplot.flierprops.markeredgecolor': 'black',
|
||||
# 'boxplot.flierprops.markeredgewidth': 1.0,
|
||||
# 'boxplot.flierprops.markerfacecolor': 'none',
|
||||
# 'boxplot.meanprops.color': 'C2',
|
||||
# 'boxplot.meanprops.markeredgecolor': 'C2',
|
||||
# 'boxplot.meanprops.markerfacecolor': 'C2',
|
||||
# 'boxplot.meanprops.markersize': 6.0,
|
||||
# 'boxplot.medianprops.color': 'C1',
|
||||
# 'boxplot.whiskerprops.color': 'black',
|
||||
'figure.edgecolor': PLT_BG_COLOR,
|
||||
'figure.facecolor': PLT_BG_COLOR,
|
||||
# 'figure.figsize': [6.4, 4.8],
|
||||
# 'figure.frameon': True,
|
||||
# 'figure.labelsize': 'large',
|
||||
'grid.color': PLT_GRID_COLOR,
|
||||
# 'hatch.color': 'black',
|
||||
'legend.edgecolor': LEGEND_BORDER_COLOR,
|
||||
'legend.facecolor': LEGEND_BG_COLOR,
|
||||
'xtick.color': PLT_FG_COLOR,
|
||||
'ytick.color': PLT_FG_COLOR,
|
||||
'xtick.labelcolor': PLT_FG_COLOR,
|
||||
'ytick.labelcolor': PLT_FG_COLOR,
|
||||
# 'lines.color': 'C0',
|
||||
'text.color': PLT_FG_COLOR,
|
||||
}
|
||||
|
||||
for k, v in color_rcParams.items():
|
||||
plt.rcParams[k] = v
|
||||
|
||||
# override single char codes
|
||||
# TODO: use color name with variant from palette instead of order
|
||||
mpl.colors.get_named_colors_mapping()["b"] = COLORS[0]
|
||||
mpl.colors.get_named_colors_mapping()["o"] = COLORS[1]
|
||||
mpl.colors.get_named_colors_mapping()["g"] = COLORS[2]
|
||||
mpl.colors.get_named_colors_mapping()["r"] = COLORS[3]
|
||||
mpl.colors.get_named_colors_mapping()["m"] = COLORS[4]
|
||||
mpl.colors.get_named_colors_mapping()["y"] = COLORS[5]
|
||||
mpl.colors.get_named_colors_mapping()["c"] = COLORS[6]
|
||||
mpl.colors.get_named_colors_mapping()["k"] = P["fg0"]
|
||||
mpl.colors.get_named_colors_mapping()["w"] = P["bg0"]
|
||||
|
||||
|
||||
|
||||
def color_latex_def(name, color):
|
||||
name = "{" + name.replace("-", "_") + "}"
|
||||
color = "{" + color.strip("#") + "}"
|
||||
return f"\\definecolor{name:10}{{HTML}}{color}"
|
||||
|
||||
def generate_latex_colorscheme(palette, variant="light"):
|
||||
s = ""
|
||||
for n, c in palette.items():
|
||||
s += color_latex_def(n, c) + "\n"
|
||||
return s
|
||||
|
||||
|
||||
|
||||
55
scripts/other/Untitled.ipynb
Normal file
55
scripts/other/Untitled.ipynb
Normal file
@ -0,0 +1,55 @@
|
||||
{
|
||||
"cells": [
|
||||
{
|
||||
"cell_type": "code",
|
||||
"execution_count": 1,
|
||||
"id": "790c45a0-a10a-411d-bfc0-bdd52e2c2492",
|
||||
"metadata": {},
|
||||
"outputs": [],
|
||||
"source": [
|
||||
"import tikz as t"
|
||||
]
|
||||
},
|
||||
{
|
||||
"cell_type": "code",
|
||||
"execution_count": 2,
|
||||
"id": "6c5d640f-c287-4e8d-a0c8-8a8d801b6fae",
|
||||
"metadata": {},
|
||||
"outputs": [],
|
||||
"source": [
|
||||
"pic = t.Picture()"
|
||||
]
|
||||
},
|
||||
{
|
||||
"cell_type": "code",
|
||||
"execution_count": null,
|
||||
"id": "9b7f8347-1619-40cd-b864-24840901e7a1",
|
||||
"metadata": {},
|
||||
"outputs": [],
|
||||
"source": [
|
||||
"pic.draw(t.node("
|
||||
]
|
||||
}
|
||||
],
|
||||
"metadata": {
|
||||
"kernelspec": {
|
||||
"display_name": "conda",
|
||||
"language": "python",
|
||||
"name": "conda"
|
||||
},
|
||||
"language_info": {
|
||||
"codemirror_mode": {
|
||||
"name": "ipython",
|
||||
"version": 3
|
||||
},
|
||||
"file_extension": ".py",
|
||||
"mimetype": "text/x-python",
|
||||
"name": "python",
|
||||
"nbconvert_exporter": "python",
|
||||
"pygments_lexer": "ipython3",
|
||||
"version": "3.12.3"
|
||||
}
|
||||
},
|
||||
"nbformat": 4,
|
||||
"nbformat_minor": 5
|
||||
}
|
||||
565
scripts/other/crystal_lattices.ipynb
Normal file
565
scripts/other/crystal_lattices.ipynb
Normal file
File diff suppressed because one or more lines are too long
@ -1,9 +1,10 @@
|
||||
#!/usr/bin env python3
|
||||
"""
|
||||
Script to process the periodic table as json into latex stuff
|
||||
Source for `elements.json` is this amazing project:
|
||||
https://pse-info.de/de/data
|
||||
|
||||
Copyright Matthias Quintern 2024
|
||||
Copyright Matthias Quintern 2025
|
||||
"""
|
||||
import json
|
||||
import os
|
||||
@ -13,7 +14,7 @@ outdir = "../src/ch"
|
||||
|
||||
|
||||
def gen_periodic_table():
|
||||
with open("elements.json") as file:
|
||||
with open("other/elements.json") as file:
|
||||
ptab = json.load(file)
|
||||
# print(ptab["elements"][1])
|
||||
s = "% This file was created by the periodic_table.py script.\n% Do not edit manually. Any changes might get lost.\n"
|
||||
@ -46,7 +47,7 @@ def gen_periodic_table():
|
||||
temp = ""
|
||||
add_refractive_index = lambda idx: f"\\GT{{{idx['label']}}}: ${idx['value']}$, "
|
||||
idxs = get("optical", "refractive_index")
|
||||
print(idxs)
|
||||
# print(idxs)
|
||||
if type(idxs) == list:
|
||||
for idx in idxs: add_refractive_index(idx)
|
||||
elif type(idxs) == dict: add_refractive_index(idxs)
|
||||
@ -64,7 +65,7 @@ def gen_periodic_table():
|
||||
el_s += f"{match.groups()[1]}}}"
|
||||
|
||||
el_s += "\n\\end{element}"
|
||||
print(el_s)
|
||||
# print(el_s)
|
||||
s += el_s + "\n"
|
||||
# print(s)
|
||||
return s
|
||||
|
||||
@ -1,36 +0,0 @@
|
||||
import os
|
||||
import matplotlib.pyplot as plt
|
||||
import numpy as np
|
||||
import math
|
||||
import scipy as scp
|
||||
|
||||
outdir = "../src/img/"
|
||||
filetype = ".pdf"
|
||||
skipasserts = False
|
||||
|
||||
full = 8
|
||||
size_half_half = (full/2, full/2)
|
||||
size_third_half = (full/3, full/2)
|
||||
size_half_third = (full/2, full/3)
|
||||
|
||||
def texvar(var, val, math=True):
|
||||
s = "$" if math else ""
|
||||
s += f"\\{var} = {val}"
|
||||
if math: s += "$"
|
||||
return s
|
||||
|
||||
def export(fig, name, notightlayout=False):
|
||||
if not skipasserts:
|
||||
assert os.path.abspath(".").endswith("scripts"), "Please run from the `scripts` directory"
|
||||
filename = os.path.join(outdir, name + filetype)
|
||||
if not notightlayout:
|
||||
fig.tight_layout()
|
||||
fig.savefig(filename) #, bbox_inches="tight")
|
||||
|
||||
|
||||
@np.vectorize
|
||||
def smooth_step(x: float, left_edge: float, right_edge: float):
|
||||
x = (x - left_edge) / (right_edge - left_edge)
|
||||
if x <= 0: return 0.
|
||||
elif x >= 1: return 1.
|
||||
else: return 3*(x**2) - 2*(x**3)
|
||||
@ -1,4 +1,4 @@
|
||||
from plot import *
|
||||
from formulasheet import *
|
||||
import scqubits as scq
|
||||
import qutip as qt
|
||||
|
||||
@ -23,33 +23,36 @@ def _plot_transmon_n_wavefunctions(qubit: scq.Transmon, fig_ax, which=[0,1]):
|
||||
ax.set_xlim(*xlim)
|
||||
ax.set_xticks(np.arange(xlim[0], xlim[1]+1))
|
||||
|
||||
def _plot_transmon(qubit: scq.Transmon, ngs, fig, axs):
|
||||
def _plot_transmon(qubit: scq.Transmon, ngs, fig, axs, wavefunction=True):
|
||||
_,_ = qubit.plot_evals_vs_paramvals("ng", ngs, fig_ax=(fig, axs[0]), evals_count=5, subtract_ground=False)
|
||||
_,_ = qubit.plot_wavefunction(fig_ax=(fig, axs[1]), which=[0, 1, 2], mode="abs_sqr")
|
||||
_plot_transmon_n_wavefunctions(qubit, (fig, axs[2]), which=[0, 1, 2])
|
||||
qubit.ng = 0.5
|
||||
_plot_transmon_n_wavefunctions(qubit, (fig, axs[3]), which=[0, 1, 2])
|
||||
qubit.ng = 0
|
||||
if wavefunction:
|
||||
_,_ = qubit.plot_wavefunction(fig_ax=(fig, axs[1]), which=[0, 1, 2], mode="abs_sqr")
|
||||
_plot_transmon_n_wavefunctions(qubit, (fig, axs[2]), which=[0, 1, 2])
|
||||
qubit.ng = 0.5
|
||||
_plot_transmon_n_wavefunctions(qubit, (fig, axs[3]), which=[0, 1, 2])
|
||||
qubit.ng = 0
|
||||
|
||||
|
||||
def transmon_cpb():
|
||||
def transmon_cpb(wavefunction=True):
|
||||
EC = 1
|
||||
qubit = scq.Transmon(EJ=30, EC=EC, ng=0, ncut=30)
|
||||
ngs = np.linspace(-2, 2, 200)
|
||||
fig, axs = plt.subplots(4, 3, squeeze=True, figsize=(full,full))
|
||||
nrows = 4 if wavefunction else 1
|
||||
|
||||
fig, axs = plt.subplots(nrows, 3, squeeze=False, figsize=(full,full/3))
|
||||
axs = axs.T
|
||||
qubit.ng = 0
|
||||
qubit.EJ = 0.1 * EC
|
||||
title = lambda x: f"$E_J/E_C = {x}$"
|
||||
_plot_transmon(qubit, ngs, fig, axs[0])
|
||||
_plot_transmon(qubit, ngs, fig, axs[0], wavefunction=wavefunction)
|
||||
axs[0][0].set_title("Cooper-Pair-Box\n"+title(qubit.EJ))
|
||||
|
||||
qubit.EJ = EC
|
||||
_plot_transmon(qubit, ngs, fig, axs[1])
|
||||
_plot_transmon(qubit, ngs, fig, axs[1], wavefunction=wavefunction)
|
||||
axs[1][0].set_title("Quantronium\n"+title(qubit.EJ))
|
||||
|
||||
qubit.EJ = 20 * EC
|
||||
_plot_transmon(qubit, ngs, fig, axs[2])
|
||||
_plot_transmon(qubit, ngs, fig, axs[2], wavefunction=wavefunction)
|
||||
axs[2][0].set_title("Transmon\n"+title(qubit.EJ))
|
||||
|
||||
for ax in axs[1:,:].flatten(): ax.set_ylabel("")
|
||||
@ -58,15 +61,14 @@ def transmon_cpb():
|
||||
ax.set_xticklabels(["-2", "-1", "", "0", "", "1", "2"])
|
||||
ylim = ax.get_ylim()
|
||||
ax.vlines([-1, -0.5], ymin=ylim[0], ymax=ylim[1], color="#aaa", linestyle="dotted")
|
||||
axs[0][2].legend()
|
||||
# axs[0][2].legend()
|
||||
fig.tight_layout()
|
||||
return fig
|
||||
|
||||
export(transmon_cpb(), "qubit_transmon")
|
||||
|
||||
|
||||
def flux_onium():
|
||||
fig, axs = plt.subplots(1, 3, squeeze=True, figsize=(full,full/2))
|
||||
fig, axs = plt.subplots(1, 3, squeeze=True, figsize=(full,full/3))
|
||||
fluxs = np.linspace(0.4, 0.6, 50)
|
||||
EJ = 35.0
|
||||
alpha = 0.3
|
||||
@ -100,4 +102,6 @@ def flux_onium():
|
||||
axs[2].set_title("Fluxonium")
|
||||
return fig
|
||||
|
||||
export(flux_onium(), "qubit_flux_onium")
|
||||
if __name__ == "__main__":
|
||||
export(transmon_cpb(wavefunction=False), "qubit_transmon")
|
||||
export(flux_onium(), "qubit_flux_onium")
|
||||
|
||||
9
scripts/readme.md
Normal file
9
scripts/readme.md
Normal file
@ -0,0 +1,9 @@
|
||||
# Scripts
|
||||
Put all scripts that generate plots or tex files here.
|
||||
|
||||
## Plots
|
||||
For plots with `matplotlib`:
|
||||
1. import `plot.py`
|
||||
2. use one of the preset figsizes
|
||||
3. save the image using the `export` function in the `if __name__ == '__main__'` part
|
||||
|
||||
@ -1,4 +1,5 @@
|
||||
numpy
|
||||
scipy
|
||||
matplotlib
|
||||
scqubits
|
||||
qutip
|
||||
|
||||
@ -1,4 +1,5 @@
|
||||
from plot import *
|
||||
#!/usr/bin env python3
|
||||
from formulasheet import *
|
||||
|
||||
def flennard_jones(r, epsilon, sigma):
|
||||
return 4 * epsilon * ((sigma/r)**12 - (sigma/r)**6)
|
||||
@ -17,7 +18,6 @@ def lennard_jones():
|
||||
ax.legend()
|
||||
ax.set_ylim(-1.1, 1.1)
|
||||
return fig
|
||||
export(lennard_jones(), "potential_lennard_jones")
|
||||
|
||||
# BOLTZMANN / FERMI-DIRAC / BOSE-EINSTEN DISTRIBUTIONS
|
||||
def fboltzmann(x):
|
||||
@ -45,7 +45,6 @@ def id_qgas():
|
||||
ax.legend()
|
||||
ax.set_ylim(-0.1, 4)
|
||||
return fig
|
||||
export(id_qgas(), "td_id_qgas_distributions")
|
||||
|
||||
@np.vectorize
|
||||
def fstep(x):
|
||||
@ -67,7 +66,6 @@ def fermi_occupation():
|
||||
ax.legend()
|
||||
ax.set_ylim(-0.1, 1.1)
|
||||
return fig
|
||||
export(fermi_occupation(), "td_fermi_occupation")
|
||||
|
||||
def fermi_heat_capacity():
|
||||
fig, ax = plt.subplots(figsize=size_half_third)
|
||||
@ -83,8 +81,8 @@ def fermi_heat_capacity():
|
||||
|
||||
|
||||
low_temp_Cv = linear(x)
|
||||
ax.plot(x, low_temp_Cv, color="orange", linestyle="dashed", label=r"${\pi^2}/{2}\,{T}/{T_\text{F}}$")
|
||||
ax.hlines([3/2], xmin=0, xmax=10, color="blue", linestyle="dashed", label="Petit-Dulong")
|
||||
ax.plot(x, low_temp_Cv, color="o", linestyle="dashed", label=r"${\pi^2}/{2}\,{T}/{T_\text{F}}$")
|
||||
ax.hlines([3/2], xmin=0, xmax=10, color="b", linestyle="dashed", label="Petit-Dulong")
|
||||
@np.vectorize
|
||||
def unphysical_f(x):
|
||||
# exponential
|
||||
@ -104,7 +102,7 @@ def fermi_heat_capacity():
|
||||
else: return a * x
|
||||
# ax.plot(x, smoothing, label="smooth")
|
||||
y = unphysical_f(x)
|
||||
ax.plot(x, y, color="black")
|
||||
ax.plot(x, y, color="k")
|
||||
ax.legend(loc="lower right")
|
||||
|
||||
|
||||
@ -116,5 +114,9 @@ def fermi_heat_capacity():
|
||||
ax.set_xlim(0, 1.4 * T_F)
|
||||
ax.set_ylim(0, 2)
|
||||
return fig
|
||||
export(fermi_heat_capacity(), "td_fermi_heat_capacity")
|
||||
|
||||
if __name__ == '__main__':
|
||||
export(lennard_jones(), "potential_lennard_jones")
|
||||
export(fermi_heat_capacity(), "td_fermi_heat_capacity")
|
||||
export(fermi_occupation(), "td_fermi_occupation")
|
||||
export(id_qgas(), "td_id_qgas_distributions")
|
||||
|
||||
190
scripts/util/colorschemes.py
Normal file
190
scripts/util/colorschemes.py
Normal file
@ -0,0 +1,190 @@
|
||||
"""
|
||||
A colorscheme for this project needs:
|
||||
fg and bg 0-4, where 0 is used as default font / background
|
||||
fg-<color> and bg-<color> where <color> is "red", "orange", "yellow", "green", "aqua", "blue", "purple", "gray"
|
||||
"""
|
||||
|
||||
from math import floor
|
||||
|
||||
|
||||
colors = ["red", "orange", "yellow", "green", "aqua", "blue", "purple", "gray"]
|
||||
|
||||
def brightness(color:str, percent:float):
|
||||
if color.startswith("#"):
|
||||
color = color.strip("#")
|
||||
newcolor = "#"
|
||||
else:
|
||||
newcolor = ""
|
||||
for i in range(3):
|
||||
c = float(int(color[i*2:i*2+2], 16))
|
||||
c = int(round(max(0, min(c*percent, 0xff)), 0))
|
||||
newcolor += f"{c:02x}"
|
||||
return newcolor
|
||||
|
||||
#
|
||||
# GRUVBOX
|
||||
#
|
||||
p_gruvbox = {
|
||||
"fg0": "#282828",
|
||||
"fg0-hard": "#1d2021",
|
||||
"fg0-soft": "#32302f",
|
||||
"fg1": "#3c3836",
|
||||
"fg2": "#504945",
|
||||
"fg3": "#665c54",
|
||||
"fg4": "#7c6f64",
|
||||
"bg0": "#fbf1c7",
|
||||
"bg0-hard": "#f9f5d7",
|
||||
"bg0-soft": "#f2e5bc",
|
||||
"bg1": "#ebdbb2",
|
||||
"bg2": "#d5c4a1",
|
||||
"bg3": "#bdae93",
|
||||
"bg4": "#a89984",
|
||||
"dark-red": "#cc241d",
|
||||
"dark-green": "#98971a",
|
||||
"dark-yellow": "#d79921",
|
||||
"dark-blue": "#458588",
|
||||
"dark-purple": "#b16286",
|
||||
"dark-aqua": "#689d6a",
|
||||
"dark-orange": "#d65d0e",
|
||||
"dark-gray": "#928374",
|
||||
"light-red": "#fb4934",
|
||||
"light-green": "#b8bb26",
|
||||
"light-yellow": "#fabd2f",
|
||||
"light-blue": "#83a598",
|
||||
"light-purple": "#d3869b",
|
||||
"light-aqua": "#8ec07c",
|
||||
"light-orange": "#f38019",
|
||||
"light-gray": "#a89984",
|
||||
"alt-red": "#9d0006",
|
||||
"alt-green": "#79740e",
|
||||
"alt-yellow": "#b57614",
|
||||
"alt-blue": "#076678",
|
||||
"alt-purple": "#8f3f71",
|
||||
"alt-aqua": "#427b58",
|
||||
"alt-orange": "#af3a03",
|
||||
"alt-gray": "#7c6f64",
|
||||
}
|
||||
|
||||
def grubox_light():
|
||||
GRUVBOX_LIGHT = { "fg0": p_gruvbox["fg0-hard"], "bg0": p_gruvbox["bg0-hard"] } \
|
||||
| {f"fg{n}": p_gruvbox[f"fg{n}"] for n in range(1,5)} \
|
||||
| {f"bg{n}": p_gruvbox[f"bg{n}"] for n in range(1,5)} \
|
||||
| {f"fg-{n}": p_gruvbox[f"alt-{n}"] for n in colors} \
|
||||
| {f"bg-{n}": p_gruvbox[f"light-{n}"] for n in colors}
|
||||
return GRUVBOX_LIGHT
|
||||
|
||||
def gruvbox_dark():
|
||||
GRUVBOX_DARK = { "fg0": p_gruvbox["bg0-hard"], "bg0": p_gruvbox["fg0-hard"] } \
|
||||
| {f"fg{n}": p_gruvbox[f"bg{n}"] for n in range(1,5)} \
|
||||
| {f"bg{n}": p_gruvbox[f"fg{n}"] for n in range(1,5)} \
|
||||
| {f"fg-{n}": p_gruvbox[f"light-{n}"] for n in colors} \
|
||||
| {f"bg-{n}": p_gruvbox[f"dark-{n}"] for n in colors}
|
||||
return GRUVBOX_DARK
|
||||
|
||||
#
|
||||
# LEGACY
|
||||
#
|
||||
p_legacy = {
|
||||
"fg0": "#fcfcfc",
|
||||
"bg0": "#333333",
|
||||
"red": "#d12229",
|
||||
"green": "#007940",
|
||||
"yellow": "#ffc615",
|
||||
"blue": "#2440fe",
|
||||
"purple": "#4D1037",
|
||||
"aqua": "#008585",
|
||||
"orange": "#f68a1e",
|
||||
"gray": "#928374",
|
||||
}
|
||||
|
||||
def legacy():
|
||||
LEGACY = \
|
||||
{ f"fg{n}": brightness(p_legacy["fg0"], 1-n/8) for n in range(5)} \
|
||||
| { f"bg{n}": brightness(p_legacy["bg0"], 1+n/8) for n in range(5)} \
|
||||
| { f"bg-{n}": c for n,c in p_legacy.items() } \
|
||||
| { f"fg-{n}": brightness(c, 2.0) for n,c in p_legacy.items() }
|
||||
return LEGACY
|
||||
|
||||
#
|
||||
# TUM
|
||||
#
|
||||
p_tum = {
|
||||
"dark-blue": "#072140",
|
||||
"light-blue": "#5E94D4",
|
||||
"alt-blue": "#3070B3",
|
||||
"light-yellow": "#FED702",
|
||||
"dark-yellow": "#CBAB01",
|
||||
"alt-yellow": "#FEDE34",
|
||||
"light-orange": "#F7811E",
|
||||
"dark-orange": "#D99208",
|
||||
"alt-orange": "#F9BF4E",
|
||||
"light-purple": "#B55CA5",
|
||||
"dark-purple": "#9B468D",
|
||||
"alt-purple": "#C680BB",
|
||||
"light-red": "#EA7237",
|
||||
"dark-red": "#D95117",
|
||||
"alt-red": "#EF9067",
|
||||
"light-green": "#9FBA36",
|
||||
"dark-green": "#7D922A",
|
||||
"alt-green": "#B6CE55",
|
||||
"light-gray": "#475058",
|
||||
"dark-gray": "#20252A",
|
||||
"alt-gray": "#333A41",
|
||||
"light-aqua": "#689d6a",
|
||||
"dark-aqua": "#427b58", # taken aquas from gruvbox
|
||||
"fg0-hard": "#000000",
|
||||
"fg0": "#000000",
|
||||
"fg0-soft": "#20252A",
|
||||
"fg1": "#072140",
|
||||
"fg2": "#333A41",
|
||||
"fg3": "#475058",
|
||||
"fg4": "#6A757E",
|
||||
"bg0-hard": "#FFFFFF",
|
||||
"bg0": "#FBF9FA",
|
||||
"bg0-soft": "#EBECEF",
|
||||
"bg1": "#DDE2E6",
|
||||
"bg2": "#E3EEFA",
|
||||
"bg3": "#F0F5FA",
|
||||
}
|
||||
|
||||
def tum():
|
||||
TUM = {}
|
||||
for n,c in p_tum.items():
|
||||
n2 = n.replace("light", "bg").replace("dark", "fg")
|
||||
TUM[n2] = c
|
||||
return TUM
|
||||
|
||||
#
|
||||
# STUPID
|
||||
#
|
||||
p_stupid = {
|
||||
"bg0": "#0505aa",
|
||||
"fg0": "#ffffff",
|
||||
"red": "#ff0000",
|
||||
"green": "#23ff81",
|
||||
"yellow": "#ffff00",
|
||||
"blue": "#5555ff",
|
||||
"purple": "#b00b69",
|
||||
"aqua": "#00ffff",
|
||||
"orange": "#ffa500",
|
||||
"gray": "#444444",
|
||||
}
|
||||
def stupid():
|
||||
LEGACY = \
|
||||
{ f"fg{n}": brightness(p_stupid["fg0"], 1-n/8) for n in range(5)} \
|
||||
| { f"bg{n}": brightness(p_stupid["bg0"], 1+n/8) for n in range(5)} \
|
||||
| { f"bg-{n}": c for n,c in p_stupid.items() } \
|
||||
| { f"fg-{n}": brightness(c, 2.0) for n,c in p_stupid.items() }
|
||||
return LEGACY
|
||||
|
||||
# UTILITY
|
||||
def color_latex_def(name, color):
|
||||
# name = name.replace("-", "_")
|
||||
color = color.strip("#")
|
||||
return "\\definecolor{" + name + "}{HTML}{" + color + "}"
|
||||
|
||||
def generate_latex_colorscheme(palette, variant="light"):
|
||||
s = ""
|
||||
for n, c in palette.items():
|
||||
s += color_latex_def(n, c) + "\n"
|
||||
return s
|
||||
84
scripts/util/mpl_colorscheme.py
Normal file
84
scripts/util/mpl_colorscheme.py
Normal file
@ -0,0 +1,84 @@
|
||||
"""
|
||||
Set the colorscheme for matplotlib plots and latex.
|
||||
|
||||
Calling this script generates util/colorscheme.tex containing xcolor definitions.
|
||||
"""
|
||||
import matplotlib as mpl
|
||||
import matplotlib.pyplot as plt
|
||||
from cycler import cycler
|
||||
|
||||
# default order for matplotlib
|
||||
color_order = ["blue", "orange", "green", "red", "purple", "yellow", "aqua", "gray"]
|
||||
|
||||
def set_mpl_colorscheme(palette: dict[str, str]):
|
||||
P = palette
|
||||
FIG_BG_COLOR = P["bg0"]
|
||||
PLT_FG_COLOR = P["fg0"]
|
||||
PLT_BG_COLOR = P["bg0"]
|
||||
PLT_GRID_COLOR = P["bg2"]
|
||||
LEGEND_FG_COLOR = PLT_FG_COLOR
|
||||
LEGEND_BG_COLOR = P["bg1"]
|
||||
LEGEND_BORDER_COLOR = P["bg2"]
|
||||
COLORS = [P[f"fg-{c}"] for c in color_order]
|
||||
|
||||
|
||||
color_rcParams = {
|
||||
'axes.edgecolor': PLT_FG_COLOR,
|
||||
'axes.facecolor': PLT_BG_COLOR,
|
||||
'axes.labelcolor': PLT_FG_COLOR,
|
||||
'axes.titlecolor': 'auto',
|
||||
# 'axes.prop_cycle': cycler('color', ['#1f77b4', '#ff7f0e', '#2ca02c', '#d62728', '#9467bd', '#8c564b', '#e377c2', '#7f7f7f', '#bcbd22', '#17becf']),
|
||||
'axes.prop_cycle': cycler('color', COLORS),
|
||||
# 'axes3d.xaxis.panecolor': (0.95, 0.95, 0.95, 0.5),
|
||||
# 'axes3d.yaxis.panecolor': (0.9, 0.9, 0.9, 0.5),
|
||||
# 'axes3d.zaxis.panecolor': (0.925, 0.925, 0.925, 0.5),
|
||||
# 'boxplot.boxprops.color': 'black',
|
||||
# 'boxplot.capprops.color': 'black',
|
||||
# 'boxplot.flierprops.color': 'black',
|
||||
# 'boxplot.flierprops.markeredgecolor': 'black',
|
||||
# 'boxplot.flierprops.markeredgewidth': 1.0,
|
||||
# 'boxplot.flierprops.markerfacecolor': 'none',
|
||||
# 'boxplot.meanprops.color': 'C2',
|
||||
# 'boxplot.meanprops.markeredgecolor': 'C2',
|
||||
# 'boxplot.meanprops.markerfacecolor': 'C2',
|
||||
# 'boxplot.meanprops.markersize': 6.0,
|
||||
# 'boxplot.medianprops.color': 'C1',
|
||||
# 'boxplot.whiskerprops.color': 'black',
|
||||
'figure.edgecolor': PLT_BG_COLOR,
|
||||
'figure.facecolor': PLT_BG_COLOR,
|
||||
# 'figure.figsize': [6.4, 4.8],
|
||||
# 'figure.frameon': True,
|
||||
# 'figure.labelsize': 'large',
|
||||
'grid.color': PLT_GRID_COLOR,
|
||||
# 'hatch.color': 'black',
|
||||
'legend.edgecolor': LEGEND_BORDER_COLOR,
|
||||
'legend.facecolor': LEGEND_BG_COLOR,
|
||||
'xtick.color': PLT_FG_COLOR,
|
||||
'ytick.color': PLT_FG_COLOR,
|
||||
'xtick.labelcolor': PLT_FG_COLOR,
|
||||
'ytick.labelcolor': PLT_FG_COLOR,
|
||||
# 'lines.color': 'C0',
|
||||
'text.color': PLT_FG_COLOR,
|
||||
}
|
||||
|
||||
for k, v in color_rcParams.items():
|
||||
plt.rcParams[k] = v
|
||||
|
||||
# override single char codes
|
||||
# TODO: use color name with variant from palette instead of order
|
||||
mpl.colors.get_named_colors_mapping()["b"] = COLORS[0]
|
||||
mpl.colors.get_named_colors_mapping()["o"] = COLORS[1]
|
||||
mpl.colors.get_named_colors_mapping()["g"] = COLORS[2]
|
||||
mpl.colors.get_named_colors_mapping()["r"] = COLORS[3]
|
||||
mpl.colors.get_named_colors_mapping()["m"] = COLORS[4]
|
||||
mpl.colors.get_named_colors_mapping()["y"] = COLORS[5]
|
||||
mpl.colors.get_named_colors_mapping()["c"] = COLORS[6]
|
||||
mpl.colors.get_named_colors_mapping()["k"] = P["fg0"]
|
||||
mpl.colors.get_named_colors_mapping()["w"] = P["bg0"]
|
||||
mpl.colors.get_named_colors_mapping()["black"] = P["fg0"]
|
||||
for color in color_order:
|
||||
mpl.colors.get_named_colors_mapping()[color] = P[f"fg-{color}"]
|
||||
|
||||
|
||||
|
||||
|
||||
320
src/ch/ch.tex
320
src/ch/ch.tex
@ -1,23 +1,311 @@
|
||||
\Part[
|
||||
\eng{Chemie}
|
||||
\eng{Chemistry}
|
||||
\ger{Chemie}
|
||||
]{ch}
|
||||
\Section[
|
||||
\eng{Periodic table}
|
||||
\ger{Periodensystem}
|
||||
]{ptable}
|
||||
\drawPeriodicTable
|
||||
\Section[
|
||||
\eng{Periodic table}
|
||||
\ger{Periodensystem}
|
||||
]{ptable}
|
||||
\drawPeriodicTable
|
||||
|
||||
\Section[
|
||||
\eng{stuff}
|
||||
\ger{stuff}
|
||||
]{stuff}
|
||||
\begin{formula}{covalent_bond}
|
||||
\desc{Covalent bond}{}{}
|
||||
\desc[german]{Kolvalente Bindung}{}{}
|
||||
\ttxt{
|
||||
\eng{Bonds that involve sharing of electrons to form electron pairs between atoms.}
|
||||
\ger{Bindungen zwischen Atomen die durch geteilte Elektronen, welche Elektronenpaare bilden, gebildet werden.}
|
||||
\Section[
|
||||
\eng{Electrochemistry}
|
||||
\ger{Elektrochemie}
|
||||
]{el}
|
||||
|
||||
\eng[std_cell]{standard cell potential}
|
||||
\ger[std_cell]{Standardzellpotential}
|
||||
\eng[electrode_pot]{electrode potential}
|
||||
\ger[electrode_pot]{Elektrodenpotential}
|
||||
\begin{formula}{chemical_potential}
|
||||
\desc{Chemical potential}{of species $i$\\Energy involved when the particle number changes}{\QtyRef{gibbs_free_energy}, \QtyRef{amount}}
|
||||
\desc[german]{Chemisches Potential}{der Spezies $i$\\Involvierte Energie, wenn sich die Teilchenzahl ändert}{}
|
||||
\quantity{\mu}{\joule\per\mol;\joule}{is}
|
||||
\eq{
|
||||
\mu_i \equiv \pdv{G}{n_i}_{n_j\neq n_i,p,T}
|
||||
}
|
||||
\end{formula}
|
||||
|
||||
\begin{formula}{standard_chemical_potential}
|
||||
\desc{Standard chemical potential}{In equilibrium}{\QtyRef{chemical_potential}, \ConstRef{universal_gas}, \QtyRef{temperature}, \QtyRef{activity}}
|
||||
\desc[german]{Standard chemisches Potential}{}{}
|
||||
\eq{\mu_i = \mu_i^\theta + RT \Ln{a_i}}
|
||||
\end{formula}
|
||||
|
||||
\begin{formula}{chemical_equilibrium}
|
||||
\desc{Chemical equilibrium}{}{\QtyRef{chemical_potential}, \QtyRef{stoichiometric_coefficient}}
|
||||
\desc[german]{Chemisches Gleichgewicht}{}{}
|
||||
\eq{\sum_\text{\GT{products}} \nu_i \mu_i = \sum_\text{\GT{educts}} \nu_i \mu_i}
|
||||
\end{formula}
|
||||
|
||||
\begin{formula}{activity}
|
||||
\desc{Activity}{relative activity}{\QtyRef{chemical_potential}, \QtyRef{standard_chemical_potential}, \ConstRef{universal_gas}, \QtyRef{temperature}}
|
||||
\desc[german]{Aktivität}{Relative Aktivität}{}
|
||||
\quantity{a}{}{s}
|
||||
\eq{a_i = \Exp{\frac{\mu_i-\mu_i^\theta}{RT}}}
|
||||
\end{formula}
|
||||
|
||||
\begin{formula}{electrochemical_potential}
|
||||
\desc{Electrochemical potential}{Chemical potential with electrostatic contributions}{\QtyRef{chemical_potential}, $z$ valency (charge), \ConstRef{faraday}, \QtyRef{electric_scalar_potential} (Galvani Potential)}
|
||||
\desc[german]{Elektrochemisches Potential}{Chemisches Potential mit elektrostatischen Enegiebeiträgen}{\QtyRef{chemical_potential}, $z$ Ladungszahl, \ConstRef{faraday}, \QtyRef{electric_scalar_potential} (Galvanisches Potential)}
|
||||
\quantity{\muecp}{\joule\per\mol;\joule}{is}
|
||||
\eq{\muecp_i \equiv \mu_i + z_i F \phi}
|
||||
\end{formula}
|
||||
|
||||
\begin{formula}{nernst_equation}
|
||||
\desc{Nernst equation}{Elektrode potential for a half-cell reaction}{$E$ electrode potential, $E^\theta$ \gt{std_cell}, \ConstRef{universal_gas}, \ConstRef{temperature}, $z$ \qtyRef{charge_number}, \ConstRef{faraday}, \QtyRef{activity}, \QtyRef{stoichiometric_coefficient}}
|
||||
\desc[german]{Nernst-Gleichung}{Elektrodenpotential für eine Halbzellenreaktion}{}
|
||||
\eq{E = E^\theta + \frac{RT}{zF} \Ln{\frac{ \left(\prod_{i}(a_i)^{\abs{\nu_i}}\right)_\text{oxidized}}{\left(\prod_{i}(a_i)^{\abs{\nu_i}}\right)_\text{reduced}}}}
|
||||
\end{formula}
|
||||
|
||||
\begin{formula}{cell}
|
||||
\desc{Electrochemical cell}{}{}
|
||||
\desc[german]{Elektrochemische Zelle}{}{}
|
||||
\ttxt{
|
||||
\eng{
|
||||
\begin{itemize}
|
||||
\item Electrolytic cell: Uses electrical energy to force a chemical reaction
|
||||
\item Galvanic cell: Produces electrical energy through a chemical reaction
|
||||
\end{itemize}
|
||||
}
|
||||
\ger{
|
||||
\begin{itemize}
|
||||
\item Elektrolytische Zelle: Nutzt elektrische Energie um eine Reaktion zu erzwingen
|
||||
\item Galvanische Zelle: Produziert elektrische Energie durch eine chemische Reaktion
|
||||
\end{itemize}
|
||||
}
|
||||
}
|
||||
\end{formula}
|
||||
\begin{formula}{standard_cell_potential}
|
||||
\desc{Standard cell potential}{}{$\Delta_\txR G^\theta$ standard \qtyRef{gibbs_free_energy} of reaction, $n$ number of electrons, \ConstRef{faraday}}
|
||||
\desc[german]{Standard Zellpotential}{}{$\Delta_\txR G^\theta$ Standard \qtyRef{gibbs_free_energy} der Reaktion, $n$ Anzahl der Elektronen, \ConstRef{faraday}}
|
||||
\eq{E^\theta_\text{rev} = \frac{-\Delta_\txR G^\theta}{nF}}
|
||||
\end{formula}
|
||||
|
||||
\begin{formula}{she}
|
||||
\desc{Standard hydrogen electrode (SHE)}{}{}
|
||||
\desc[german]{Standard Wasserstoffelektrode}{}{}
|
||||
\ttxt{
|
||||
\eng{Defined as reference for measuring half-cell potententials}
|
||||
\ger{Definiert als Referenz für Messungen von Potentialen von Halbzellen}
|
||||
}
|
||||
$a_{\ce{H+}} =1 \, (\text{pH} = 0)$, $p_{\ce{H2}} = \SI{100}{\kilo\pascal}$
|
||||
\end{formula}
|
||||
|
||||
\eng[galvanic]{galvanic}
|
||||
\ger[galvanic]{galvanisch}
|
||||
\eng[electrolytic]{electrolytic}
|
||||
\ger[electrolytic]{electrolytisch}
|
||||
\begin{formula}{cell_efficiency}
|
||||
\desc{Thermodynamic cell efficiency}{}{$P$ \fqEqRef{ed:el:power}}
|
||||
\desc[german]{Thermodynamische Zelleffizienz}{}{}
|
||||
\eq{
|
||||
\eta_\text{cell} &= \frac{P_\text{obtained}}{P_\text{maximum}} = \frac{E_\text{cell}}{E_\text{cell,rev}} & & \text{\gt{galvanic}} \\
|
||||
\eta_\text{cell} &= \frac{P_\text{minimum}}{P_\text{applied}} = \frac{E_\text{cell,rev}}{E_\text{cell}} & & \text{\gt{electrolytic}}
|
||||
}
|
||||
\end{formula}
|
||||
|
||||
\Subsection[
|
||||
\eng{Ionic conduction in electrolytes}
|
||||
\ger{Ionische Leitung in Elektrolyten}
|
||||
]{ion_cond}
|
||||
\eng[z]{charge number}
|
||||
\ger[z]{Ladungszahl}
|
||||
\eng[of_i]{of ion $i$}
|
||||
\ger[of_i]{des Ions $i$}
|
||||
|
||||
\begin{formula}{diffusion}
|
||||
\desc{Diffusion}{caused by concentration gradients}{$z_i$ \qtyRef{charge_number} \gt{of_i}, \ConstRef{faraday}, \QtyRef{diffusion_constant} \gt{of_i}, \QtyRef{concentration} \gt{of_i}}
|
||||
\desc[german]{Diffusion}{durch Konzentrationsgradienten}{}
|
||||
\eq{ i_\text{diff} = \sum_i -z_i F D_i \left(\odv{c_i}{x}\right) }
|
||||
\end{formula}
|
||||
|
||||
\begin{formula}{migration}
|
||||
\desc{Migration}{caused by potential gradients}{$z_i$ \qtyRef{charge_number} \gt{of_i}, \ConstRef{faraday}, \QtyRef{concentration} \gt{of_i}, \QtyRef{mobility} \gt{of_i}, $\nabla\phi_\txs$ potential gradient in the solution}
|
||||
\desc[german]{Migration}{durch Potentialgradienten}{$z_i$ \qtyRef{charge_number} \gt{of_i}, \ConstRef{faraday}, \QtyRef{concentration} \gt{of_i}, \QtyRef{mobility} \gt{of_i}, $\nabla\phi_\txs$ Potentialgradient in der Lösung}
|
||||
\eq{ i_\text{mig} = \sum_i -z_i^2 F^2 \, c_i \, \mu_i \, \nabla\Phi_\txs }
|
||||
\end{formula}
|
||||
|
||||
\begin{formula}{convection}
|
||||
\desc{Convection}{caused by pressure gradients}{$z_i$ \qtyRef{charge_number} \gt{of_i}, \ConstRef{faraday}, \QtyRef{concentration} \gt{of_i}, $v_i^\text{flow}$ \qtyRef{velocity} \gt{of_i} in flowing electrolyte}
|
||||
\desc[german]{Convection}{durch Druckgradienten}{$z_i$ \qtyRef{charge_number} \gt{of_i}, \ConstRef{faraday}, \QtyRef{concentration} \gt{of_i}, $v_i^\text{flow}$ \qtyRef{velocity} \gt{of_i} im fliessenden Elektrolyt}
|
||||
\eq{ i_\text{conv} = \sum_i -z_i F \, c_i \, v_i^\text{flow} }
|
||||
\end{formula}
|
||||
|
||||
\begin{formula}{ionic_conductivity}
|
||||
\desc{Ionic conductivity}{}{\ConstRef{faraday}, $z_i$, $c_i$, $\mu_i$ charge number, \qtyRef{concentration} and \qtyRef{mobility} of the positive (+) and negative (-) ions}
|
||||
\desc[german]{Ionische Leitfähigkeit}{}{\ConstRef{faraday}, $z_i$, $c_i$, $\mu_i$ Ladungszahl, \qtyRef{concentration} und \qtyRef{mobility} der positiv (+) und negativ geladenen Ionen}
|
||||
\quantity{\kappa}{\per\ohm\cm=\siemens\per\cm}{}
|
||||
\eq{\kappa = F^2 \left(z_+^2 \, c_+ \, \mu_+ + z_-^2 \, c_- \, \mu_-\right)}
|
||||
\end{formula}
|
||||
|
||||
\begin{formula}{ionic_resistance}
|
||||
\desc{Ohmic resistance of ionic current flow}{}{$L$ \qtyRef{length}, $A$ \qtyRef{area}, \QtyRef{ionic_conductivity}}
|
||||
\desc[german]{Ohmscher Widerstand für Ionen-Strom}{}{}
|
||||
\eq{R_\Omega = \frac{L}{A\,\kappa}}
|
||||
\end{formula}
|
||||
|
||||
\begin{formula}{ionic_mobility}
|
||||
\desc{Ionic mobility}{}{$v_\pm$ steady state drift \qtyRef{velocity}, $\phi$ \qtyRef{electric_scalar_potential}, $z$ \qtyRef{charge_number}, \ConstRef{faraday}, \ConstRef{charge}, \QtyRef{viscosity}, $r_\pm$ ion radius}
|
||||
\desc[german]{Ionische Moblilität}{}{}
|
||||
\quantity{u_\pm}{\cm^2\mol\per\joule\s}{}
|
||||
% \eq{u_\pm = - \frac{v_\pm}{\nabla \phi \,z_\pm F} = \frac{e}{6\pi F \eta_\text{dyn} \r_\pm}}
|
||||
\end{formula}
|
||||
|
||||
\begin{formula}{transference}
|
||||
\desc{Transference number}{Ion transport number \\Fraction of the current carried by positive / negative ions}{$i_{+/-}$ current through positive/negative charges}
|
||||
\desc[german]{Überführungszahl}{Anteil der positiv / negativ geladenen Ionen am Gesamtstrom}{$i_{+/-}$ Strom durch positive / negative Ladungn}
|
||||
\eq{t_{+/-} = \frac{i_{+/-}}{i_+ + i_-}}
|
||||
\end{formula}
|
||||
|
||||
\eng[csalt]{electrolyte \qtyRef{concentration}}
|
||||
\eng[csalt]{\qtyRef{concentration} des Elektrolyts}
|
||||
\begin{formula}{molar_conductivity}
|
||||
\desc{Molar conductivity}{}{\QtyRef{ionic_conductivity}, $c_\text{salt}$ \gt{csalt}}
|
||||
\desc[german]{Molare Leitfähigkeit}{}{\QtyRef{ionic_conductivity}, $c_\text{salt}$ \gt{salt}}
|
||||
\quantity{\Lambda_\txM}{\siemens\cm^2\per\mol=\ampere\cm^2\per\volt\mol}{ievs}
|
||||
\eq{\Lambda_\txM = \frac{\kappa}{c_\text{salt}}}
|
||||
\end{formula}
|
||||
|
||||
\begin{formula}{kohlrausch_law}
|
||||
\desc{Kohlrausch's law}{}{$\Lambda_\txM^0$ \qtyRef{molar_conductivity} at infinite dilution, $c_\text{salt}$ \gt{csalt}, $K$ \GT{constant}}
|
||||
\desc[german]{}{}{$\Lambda_\txM^0$ \qtyRef{molar_conductivity} bei unendlicher Verdünnung, $\text{salt}$ \gt{csalt} $K$ \GT{constant}}
|
||||
\eq{\Lambda_\txM = \Lambda_\txM^0 - K \sqrt{c_\text{salt}}}
|
||||
\end{formula}
|
||||
|
||||
% Electrolyte conductivity
|
||||
\begin{formula}{molality}
|
||||
\desc{Molality}{}{\QtyRef{amount} of the solute, \QtyRef{mass} of the solvent}
|
||||
\desc[german]{Molalität}{}{\QtyRef{amount} des gelösten Stoffs, \QtyRef{mass} des Lösungsmittels}
|
||||
\quantity{b}{\mol\per\kg}{}
|
||||
\eq{b = \frac{n}{m}}
|
||||
\end{formula}
|
||||
|
||||
\begin{formula}{molarity}
|
||||
\desc{Molarity}{\GT{see} \qtyRef{concentration}}{\QtyRef{amount} of the solute, \QtyRef{volume} of the solvent}
|
||||
\desc[german]{Molarität}{}{\QtyRef{amount} des gelösten Stoffs, \QtyRef{volume} des Lösungsmittels}
|
||||
\quantity{c}{\mol\per\litre}{}
|
||||
\eq{c = \frac{n}{V}}
|
||||
\end{formula}
|
||||
|
||||
\begin{formula}{ionic_strength}
|
||||
\desc{Ionic strength}{Measure of the electric field in a solution through solved ions}{\QtyRef{molality}, \QtyRef{molarity}, $z$ \qtyRef{charge_number}}
|
||||
\desc[german]{Ionenstärke}{Maß eienr Lösung für die elektrische Feldstärke durch gelöste Ionen}{}
|
||||
\quantity{I}{\mol\per\kg;\mol\per\litre}{}
|
||||
\eq{I_b &= \frac{1}{2} \sum_i b_i z_i^2 \\ I_c &= \frac{1}{2} \sum_i c_i z_i^2}
|
||||
\end{formula}
|
||||
|
||||
\begin{formula}{debye_screening_length}
|
||||
\desc{Debye screening length}{}{\ConstRef{avogadro}, \ConstRef{charge}, \QtyRef{ionic_strength}, \QtyRef{permittivity}, \ConstRef{boltzmann}, \QtyRef{temperature}}
|
||||
\desc[german]{Debye-Länge / Abschirmlänge}{}{}
|
||||
\eq{\lambda_\txD = \sqrt{\frac{\epsilon \kB T}{2\NA e^2 I_C}}}
|
||||
\end{formula}
|
||||
|
||||
\begin{formula}{mean_ionic_activity}
|
||||
\desc{Mean ionic activity coefficient}{Accounts for decreased reactivity because ions must divest themselves of their ion cloud before reacting}{}
|
||||
\desc[german]{Mittlerer ionischer Aktivitätskoeffizient}{Berücksichtigt dass Ionen sich erst von ihrer Ionenwolke lösen müssen, bevor sie reagieren können}{}
|
||||
\quantity{\gamma}{}{s}
|
||||
\eq{\gamma_\pm = \left(\gamma_+^{\nu_+} \, \gamma_-^{\nu_-}\right)^{\frac{1}{\nu_+ + \nu_-}}}
|
||||
\end{formula}
|
||||
|
||||
\begin{formula}{debye_hueckel_law}
|
||||
\desc{Debye-Hückel limiting law}{For an infinitely dilute solution}{\QtyRef{mean_ionic_activity}, $A$ solvent dependant constant, $z$ \qtyRef{charge_number}, \QtyRef{ionic_strength} in [\si{\mol\per\kg}]}
|
||||
\desc[german]{Debye-Hückel Gesetz}{Für eine unendlich verdünnte Lösung}{}
|
||||
\eq{\Ln{\gamma_{\pm}} = -A \abs{z_+ \, z_-} \sqrt{I_b}}
|
||||
\end{formula}
|
||||
|
||||
\Subsection[
|
||||
\eng{Kinetics}
|
||||
\ger{Kinetik}
|
||||
]{kin}
|
||||
\begin{formula}{overpotential}
|
||||
\desc{Overpotential}{}{$E_\text{electrode}$ potential at which the reaction starts $E_\text{ref}$ thermodynamic potential of the reaction}
|
||||
\desc[german]{Überspannung}{}{$E_\text{electrode}$ Potential bei der die Reaktion beginnt, $E_\text{ref}$ thermodynamisches Potential der Reaktion}
|
||||
\eq{\eta_\text{act} = E_\text{electrode} - E_\text{ref}}
|
||||
\end{formula}
|
||||
|
||||
\begin{formula}{activation_overpotential}
|
||||
\desc{Activation overpotential}{}{}
|
||||
\desc[german]{Aktivierungsüberspannung}{}{}
|
||||
\eq{}
|
||||
\end{formula}
|
||||
|
||||
\begin{formula}{concentration_overpotential}
|
||||
\desc{Concentration overpotential}{}{}
|
||||
\desc[german]{Konzentrationsüberspannung}{}{}
|
||||
\eq{\eta_\text{conc} = -\frac{RT}{(1-\alpha) nF} \ln \left(\frac{c_\text{ox}^0}{c_\text{ox}^\txS}\right)}
|
||||
\end{formula}
|
||||
|
||||
\begin{formula}{diffusion_overpotential}
|
||||
\desc{Diffusionoverpotential}{}{}
|
||||
\desc[german]{Diffusionsüberspannung}{}{}
|
||||
\eq{}
|
||||
\end{formula}
|
||||
\begin{formula}{roughness_factor}
|
||||
\desc{Roughness factor}{Surface area related to electrode geometry}{}
|
||||
\eq{\rfactor}
|
||||
\end{formula}
|
||||
|
||||
\begin{formula}{butler_volmer}
|
||||
\desc{Butler-Volmer equation}{Reaction kinetics near the equilibrium potentential}
|
||||
{$j$ \qtyRef{current_density}, $j_0$ exchange current density, $\eta$ \fqEqRef{ch:el:kin:overpotential}, \QtyRef{temperature}, $z$ \qtyRef{charge_number}, \ConstRef{faraday}, \ConstRef{universal_gas}, $\alpha_{\txc/\txa}$ cathodic/anodic charge transfer coefficient}
|
||||
%Current through an electrode iof a unimolecular redox reaction with both anodic and cathodic reaction occuring on the same electrode
|
||||
\desc[german]{Butler-Volmer-Gleichung}{Reaktionskinetik in der Nähe des Gleichgewichtspotentials}
|
||||
{$j$ \qtyRef{current_density}, $j_0$ Austauschstromdichte, $\eta$ \fqEqRef{ch:el:kin:overpotential}, \QtyRef{temperature}, $z$ \qtyRef{charge_number}, \ConstRef{faraday}, \ConstRef{universal_gas}, $\alpha_{\txc/\txa}$ Ladungstransferkoeffizient an der Kathode/Anode}
|
||||
\begin{gather}
|
||||
j = j_0 \,\rfactor\, \left[ \Exp{\frac{(1-a_\txc) z F \eta}{RT}} - \Exp{-\frac{\alpha_\txc z F \eta}{RT}}\right]
|
||||
\intertext{\GT{with}}
|
||||
\alpha_\txa = 1 - \alpha_\txc
|
||||
\end{gather}
|
||||
\separateEntries
|
||||
\fig{img/ch_butler_volmer.pdf}
|
||||
\end{formula}
|
||||
|
||||
|
||||
|
||||
\Section[
|
||||
\eng{misc}
|
||||
\ger{misc}
|
||||
]{misc}
|
||||
\begin{formula}{std_condition}
|
||||
\desc{Standard temperature and pressure}{}{}
|
||||
\desc[german]{Standardbedingungen}{}{}
|
||||
\eq{
|
||||
T &= \SI{273.15}{\kelvin} = \SI{0}{\celsius} \\
|
||||
p &= \SI{100000}{\pascal} = \SI{1.000}{\bar}
|
||||
}
|
||||
\end{formula}
|
||||
\begin{formula}{ph}
|
||||
\desc{pH definition}{}{$a_{\ce{H+}}$ hyrdrogen ion \qtyRef{activity}}
|
||||
\desc[german]{pH-Wert definition}{}{$a_{\ce{H+}}$ Wasserstoffionen-\qtyRef{activity}}
|
||||
\eq{\pH = -\log_{10}(a_{\ce{H+}})}
|
||||
\end{formula}
|
||||
|
||||
\begin{formula}{ph_rt}
|
||||
\desc{pH}{At room temperature \SI{25}{\celsius}}{}
|
||||
\desc[german]{pH-Wert}{Bei Raumtemperatur \SI{25}{\celsius}}{}
|
||||
\eq{
|
||||
\pH > 7 &\quad\tGT{basic} \\
|
||||
\pH < 7 &\quad\tGT{acidic} \\
|
||||
\pH = 7 &\quad\tGT{neutral}
|
||||
}
|
||||
\end{formula}
|
||||
|
||||
\begin{formula}{covalent_bond}
|
||||
\desc{Covalent bond}{}{}
|
||||
\desc[german]{Kolvalente Bindung}{}{}
|
||||
\ttxt{
|
||||
\eng{Bonds that involve sharing of electrons to form electron pairs between atoms.}
|
||||
\ger{Bindungen zwischen Atomen die durch geteilte Elektronen, welche Elektronenpaare bilden, gebildet werden.}
|
||||
}
|
||||
\end{formula}
|
||||
|
||||
\begin{formula}{grotthuss}
|
||||
\desc{Grotthuß-mechanism}{}{}
|
||||
\desc[german]{Grotthuß-Mechanismus}{}{}
|
||||
\ttxt{
|
||||
\eng{The mobility of protons in aqueous solutions is much higher than that of other ions because they can "move" by breaking and reforming covalent bonds of water molecules.}
|
||||
\ger{The Moblilität von Protononen in wässrigen Lösungen ist wesentlich größer als die anderer Ionen, da sie sich "bewegen" können indem die Wassertsoffbrückenbindungen gelöst und neu gebildet werden.}
|
||||
}
|
||||
\end{formula}
|
||||
|
||||
|
||||
@ -3,3 +3,58 @@
|
||||
\ger{Festkörperphysik}
|
||||
]{cm}
|
||||
\TODO{Bonds, hybridized orbitals}
|
||||
\TODO{Lattice vibrations, van hove singularities, debye frequency}
|
||||
|
||||
\begin{formula}{dos}
|
||||
\desc{Density of states (DOS)}{}{\QtyRef{volume}, $N$ number of energy levels, \QtyRef{energy}}
|
||||
\desc[german]{Zustandsdichte (DOS)}{}{\QtyRef{volume}, $N$ Anzahl der Energieniveaus, \QtyRef{energy}}
|
||||
\eq{D(E) = \frac{1}{V}\sum_{i=1}^{N} \delta(E-E(\vec{k_i}))}
|
||||
\end{formula}
|
||||
\begin{formula}{dos_parabolic}
|
||||
\desc{Density of states for parabolic dispersion}{Applies to \fqSecRef{cm:egas}}{}
|
||||
\desc[german]{Zustandsdichte für parabolische Dispersion}{Bei \fqSecRef{cm:egas}}{}
|
||||
\eq{
|
||||
D_1(E) &= \frac{1}{2\sqrt{c_k(E-E_0)}} && (\text{1D}) \\
|
||||
D_2(E) &= \frac{\pi}{2c_k} && (\text{2D}) \\
|
||||
D_3(E) &= \pi \sqrt{\frac{E-E_0}{c_k^3}}&& (\text{3D})
|
||||
}
|
||||
\end{formula}
|
||||
|
||||
\Section[
|
||||
\eng{Lattice vibrations}
|
||||
\ger{Gitterschwingungen}
|
||||
]{vib}
|
||||
|
||||
\begin{formula}{dispersion_1atom_basis}
|
||||
\desc{Phonon dispersion of a lattice with a one-atom basis}{same as the dispersion of a linear chain}{$C_n$ force constants between layer $s$ and $s+n$, $M$ \qtyRef{mass} of the reference atom, $a$ \qtyRef{lattice_constant}, $q$ phonon \qtyRef{wavevector}, $u$ Ansatz for the atom displacement}
|
||||
\desc[german]{Phonondispersion eines Gitters mit zweiatomiger Basis}{gleich der Dispersion einer linearen Kette}{$C_n$ Kraftkonstanten zwischen Ebene $s$ und $s+n$, $M$ \qtyRef{mass} des Referenzatoms, $a$ \qtyRef{lattice_constant}, $q$ Phonon \qtyRef{wavevector}, $u$ Ansatz für die Atomauslenkung}
|
||||
\eq{
|
||||
\omega^2 = \frac{4C_1}{M}\left[\sin^2 \left(\frac{qa}{2}\right) + \frac{C2}{C1} \sin^2(qa)\right] \\
|
||||
\intertext{\GT{with}}
|
||||
u_{s+n} = U\e^{-i \left[\omega t - q(s+n)a \right]}
|
||||
}
|
||||
\fig{img/cm_phonon_dispersion_one_atom_basis.pdf}
|
||||
\end{formula}
|
||||
\TODO{Plots}
|
||||
\begin{formula}{dispersion_2atom_basis}
|
||||
\desc{Phonon dispersion of a lattice with a two-atom basis}{}{$C$ force constant between layers, $M_i$ \qtyRef{mass} of the basis atoms, $a$ \qtyRef{lattice_constant}, $q$ phonon \qtyRef{wavevector}, $u, v$ Ansatz for the displacement of basis atom 1 and 2, respectively}
|
||||
\desc[german]{Phonondispersion eines Gitters mit einatomiger Basis}{}{$C$ Kraftkonstanten zwischen Ebene $s$ und $s+n$, $M_i$ \qtyRef{mass} der Basisatome, $a$ \qtyRef{lattice_constant}, $q$ Phonon \qtyRef{wavevector}, $u, v$ jeweils Ansatz für die Atomauslenkung des Basisatoms 1 und 2}
|
||||
\eq{
|
||||
\omega^2_{\txa,\txo} = C \left(\frac{1}{M_1}+\frac{1}{M_2}\right) \mp C \sqrt{\left(\frac{1}{M_1}+\frac{1}{M_2}\right)^2 - \frac{4}{M_1M_2} \sin^2 \left(\frac{qa}{2}\right)}
|
||||
\intertext{\GT{with}}
|
||||
u_{s} = U\e^{-i \left(\omega t - qsa \right)}, \quad
|
||||
v_{s} = V\e^{-i \left(\omega t - qsa \right)}
|
||||
}
|
||||
\fig{img/cm_phonon_dispersion_two_atom_basis.pdf}
|
||||
\end{formula}
|
||||
|
||||
\Subsection[
|
||||
\eng{Debye model}
|
||||
\ger{Debye-Modell}
|
||||
]{debye}
|
||||
\begin{ttext}
|
||||
\eng{Atoms behave like coupled \hyperref[sec:qm:hosc]{quantum harmonic oscillators}. The finite sample size leads to periodic boundary conditio. The finite sample size leads to periodic boundary conditions for the vibrations.}
|
||||
\ger{Atome verhalten sich wie gekoppelte \hyperref[sec:qm:hosc]{quantenmechanische harmonische Oszillatoren}. Die endliche Ausdehnung des Körpers führt zu periodischen Randbedingungen. }
|
||||
\end{ttext}
|
||||
|
||||
|
||||
|
||||
@ -6,11 +6,11 @@
|
||||
\eng{Bravais lattice}
|
||||
\ger{Bravais-Gitter}
|
||||
]{bravais}
|
||||
\eng[bravais_table2]{In 2D, there are 5 different Bravais lattices}
|
||||
\ger[bravais_table2]{In 2D gibt es 5 verschiedene Bravais-Gitter}
|
||||
\eng[table2D]{In 2D, there are 5 different Bravais lattices}
|
||||
\ger[table2D]{In 2D gibt es 5 verschiedene Bravais-Gitter}
|
||||
|
||||
\eng[bravais_table3]{In 3D, there are 14 different Bravais lattices}
|
||||
\ger[bravais_table3]{In 3D gibt es 14 verschiedene Bravais-Gitter}
|
||||
\eng[table3D]{In 3D, there are 14 different Bravais lattices}
|
||||
\ger[table3D]{In 3D gibt es 14 verschiedene Bravais-Gitter}
|
||||
|
||||
\Eng[lattice_system]{Lattice system}
|
||||
\Ger[lattice_system]{Gittersystem}
|
||||
@ -26,7 +26,7 @@
|
||||
\newcolumntype{Z}{>{\centering\let\newline\\\arraybackslash\hspace{0pt}}X}
|
||||
\begin{table}[H]
|
||||
\centering
|
||||
\expandafter\caption\expandafter{\gt{bravais_table2}}
|
||||
\expandafter\caption\expandafter{\gt{table2D}}
|
||||
\label{tab:bravais2}
|
||||
|
||||
\begin{adjustbox}{width=\textwidth}
|
||||
@ -46,7 +46,7 @@
|
||||
|
||||
\begin{table}[H]
|
||||
\centering
|
||||
\caption{\gt{bravais_table3}}
|
||||
\caption{\gt{table3D}}
|
||||
\label{tab:bravais3}
|
||||
|
||||
% \newcolumntype{g}{>{\columncolor[]{0.8}}}
|
||||
|
||||
@ -95,7 +95,7 @@
|
||||
]{gl}
|
||||
\begin{ttext}
|
||||
\eng{
|
||||
|
||||
\TODO{TODO}
|
||||
}
|
||||
|
||||
\end{ttext}
|
||||
@ -132,10 +132,67 @@
|
||||
\eng{Microscopic theory}
|
||||
\ger{Mikroskopische Theorie}
|
||||
]{micro}
|
||||
|
||||
\begin{formula}{isotop_effect}
|
||||
\desc{Isotope effect}{Superconducting behaviour depends on atomic mass and thereby of the lattice \Rightarrow Microscopic origin}{$\Tcrit$ critial temperature, $M$ isotope mass, $\omega_\text{ph}$}
|
||||
\desc[german]{Isotopeneffekt}{Supraleitung hängt von der Atommasse und daher von den Gittereigenschaften ab \Rightarrow Mikroskopischer Ursprung}{$\Tcrit$ kritische Temperatur, $M$ Isotopen-Masse, $\omega_\text{ph}$}
|
||||
\eq{
|
||||
\Tcrit \propto \frac{1}{\sqrt{M}} \\
|
||||
\omega_\text{ph} \propto \frac{1}{\sqrt{M}} \Rightarrow \Tcrit \propto \omega_\text{ph}
|
||||
}
|
||||
\end{formula}
|
||||
|
||||
\begin{formula}{cooper_pairs}
|
||||
\desc{Cooper pairs}{}{}
|
||||
\desc[german]{Cooper-Paars}{}{}
|
||||
\ttxt{
|
||||
\eng{Conduction electrons reduce their energy through an attractive interaction: One electron passing by atoms attracts the these, which creats a positive charge region behind the electron, which in turn attracts another electron. }
|
||||
}
|
||||
\end{formula}
|
||||
|
||||
\Subsection[
|
||||
\Subsubsection[
|
||||
\eng{BCS-Theory}
|
||||
\ger{BCS-Theorie}
|
||||
]{BCS}
|
||||
|
||||
]{bcs}
|
||||
\begin{ttext}
|
||||
\eng{
|
||||
Electron pairs form bosonic quasi-particles called Cooper pairs which can condensate into the ground state.
|
||||
The wave function spans the whole material, which makes it conduct without resistance.
|
||||
The exchange bosons between the electrons are phonons.
|
||||
}
|
||||
\ger{
|
||||
Elektronenpaar bilden bosonische Quasipartikel (Cooper Paare) welche in den Grundzustand kondensieren können.
|
||||
Die Wellenfunktion übersoannt den gesamten Festkörper, was einen widerstandslosen Ladungstransport garantiert.
|
||||
Die Austauschbosononen zwischen den Elektronen sind Bosonen.
|
||||
}
|
||||
\end{ttext}
|
||||
\def\BCS{{\text{BCS}}}
|
||||
\begin{formula}{hamiltonian}
|
||||
\desc{BCS Hamiltonian}{for $N$ interacting electrons}{
|
||||
$c_{\veck\sigma}$ creation/annihilation operators create/destroy at $\veck$ with spin $\sigma$ \\
|
||||
First term: non-interacting free electron gas\\
|
||||
Second term: interaction energy
|
||||
}
|
||||
\desc[german]{BCS Hamiltonian}{}{}
|
||||
\eq{
|
||||
\hat{H}_\BCS =
|
||||
\sum_{\sigma} \sum_\veck \epsilon_\veck \hat{c}_{\veck\sigma}^\dagger \hat{c}_{\veck\sigma}
|
||||
+ \sum_{\veck,\veck^\prime} V_{\veck,\veck^\prime}
|
||||
\hat{c}_{\veck\uparrow}^\dagger \hat{c}_{-\veck\downarrow}^\dagger
|
||||
\hat{c}_{-\veck^\prime\downarrow} \hat{c}_{\veck^\prime,\uparrow}
|
||||
}
|
||||
\end{formula}
|
||||
|
||||
\begin{formula}{bogoliubov-valatin}
|
||||
\desc{Bogoliubov-Valatin transformation}{Diagonalization of the \fqEqRef{cm:sc:micro:bcs:hamiltonian} to derive excitation energies}{}
|
||||
\desc[german]{Bogoliubov-Valatin transformation}{}{}
|
||||
\eq{
|
||||
\hat{H}_\BCS - N\mu = \sum_\veck \big[\xi_\veck - E_\veck + \Delta_\veck g_\veck^*\big] + \sum_\veck \big[E_\veck a_\veck^\dagger a_\veck + E_\veck \beta_{-\veck}^\dagger \beta_{-\veck}\big]
|
||||
}
|
||||
\end{formula}
|
||||
|
||||
\begin{formula}{gap_equation}
|
||||
\desc{BCS-gap equation}{}{}
|
||||
\desc[german]{}{}{}
|
||||
\eq{\Delta_\veck^* = -\sum_\veck^+\prime V_{\veck,\veck^\prime} \frac{\Delta_{\veck^\prime}}{2E_\veck} \tanh \left(\frac{E_{\veck^\prime}}{2\kB T}\right)}
|
||||
\end{formula}
|
||||
|
||||
14
src/cm/mat.tex
Normal file
14
src/cm/mat.tex
Normal file
@ -0,0 +1,14 @@
|
||||
\Section[
|
||||
\eng{Material physics}
|
||||
\ger{Materialphysik}
|
||||
]{mat}
|
||||
|
||||
\begin{formula}{tortuosity}
|
||||
\desc{Tortuosity}{Degree of the winding of a transport path through a porous material. \\ Multiple definitions exist}{$l$ path length, $L$ distance of the end points}
|
||||
\desc[german]{Toruosität}{Grad der Gewundenheit eines Transportweges in einem porösen Material. \\ Mehrere Definitionen existieren}{$l$ Weglänge, $L$ Distanz der Endpunkte}
|
||||
\quantity{\tau}{}{}
|
||||
\eq{
|
||||
\tau &= \left(\frac{l}{L}\right)^2 \\
|
||||
\tau &= \frac{l}{L}
|
||||
}
|
||||
\end{formula}
|
||||
@ -84,19 +84,27 @@
|
||||
\ger{\GT{misc}}
|
||||
]{misc}
|
||||
|
||||
\begin{formula}{exciton}
|
||||
\desc{Exciton}{}{}
|
||||
\desc[german]{Exziton}{}{}
|
||||
\ttxt{
|
||||
\eng{Quasi particle, excitation in condensed matter as bound electron-hole pair.}
|
||||
\ger{Quasiteilchen, Anregung im Festkörper als gebundenes Elektron-Loch-Paar}
|
||||
}
|
||||
\end{formula}
|
||||
|
||||
|
||||
\begin{formula}{work_function}
|
||||
\desc{Work function}{Lowest energy required to remove an electron into the vacuum}{}
|
||||
\desc[german]{Austrittsarbeit}{eng. "Work function"; minimale Energie um ein Elektron aus dem Festkörper zu lösen}{}
|
||||
\quantity{W}{\eV}{s}
|
||||
\eq{-e\phi - \EFermi}
|
||||
\eq{W = \Evac - \EFermi}
|
||||
\end{formula}
|
||||
|
||||
\begin{formula}{electron_affinity}
|
||||
\desc{Electron affinity}{Energy required to remove one electron from an anion with one negative charge.\\Energy difference between vacuum level and conduction band}{}
|
||||
\desc[german]{Elektronenaffinität}{Energie, die benötigt wird um ein Elektron aus einem einfach-negativ geladenen Anion zu entfernen. Entspricht der Energiedifferenz zwischen Vakuum-Niveau und dem Leitungsband}{}
|
||||
\quantity{\chi}{\eV}{s}
|
||||
\eq{\chi = \left(\Evac - \Econd\right)}
|
||||
\end{formula}
|
||||
|
||||
|
||||
\begin{formula}{laser}
|
||||
\desc{Laser}{Light amplification by stimulated emission of radiation}{}
|
||||
\desc[german]{Laser}{}{}
|
||||
\ttxt{
|
||||
\eng{\textit{Gain medium} is energized \textit{pumping energy} (electric current or light), light of certain wavelength is amplified in the gain medium}
|
||||
}
|
||||
\end{formula}
|
||||
|
||||
@ -2,44 +2,47 @@
|
||||
\eng{Semiconductors}
|
||||
\ger{Halbleiter}
|
||||
]{semic}
|
||||
\begin{formula}{types}
|
||||
\desc{Intrinsic/extrinsic}{}{$n,p$ \fqEqRef{cm:semic:charge_density_eq}}
|
||||
\desc[german]{Intrinsisch/Extrinsisch}{}{}
|
||||
\ttxt{
|
||||
\eng{
|
||||
Intrinsic: pure, electron density determiend only by thermal excitation and $n_i^2 = n_0 p_0$\\
|
||||
Extrinsic: doped
|
||||
}
|
||||
\ger{
|
||||
Intrirnsisch: Pur, Elektronendichte gegeben durch thermische Anregung und $n_i^2 = n_0 p_0$ \\
|
||||
Extrinsisch: gedoped
|
||||
}
|
||||
\begin{formula}{types}
|
||||
\desc{Intrinsic/extrinsic}{}{$n,p$ \fqEqRef{cm:semic:charge_density_eq}}
|
||||
\desc[german]{Intrinsisch/Extrinsisch}{}{}
|
||||
\ttxt{
|
||||
\eng{
|
||||
Intrinsic: pure, electron density determiend only by thermal excitation and $n_i^2 = n_0 p_0$\\
|
||||
Extrinsic: doped
|
||||
}
|
||||
\end{formula}
|
||||
|
||||
\begin{formula}{charge_density_eq}
|
||||
\desc{Equilibrium charge densitites}{Holds when $\frac{\Econd-\EFermi}{\kB T}>3.6$ and $\frac{\EFermi-\Evalence}{\kB T} > 3.6$}{}
|
||||
\desc[german]{Ladungsträgerdichte im Equilibrium}{Gilt wenn $\frac{\Econd-\EFermi}{\kB T}>3.6$ und $\frac{\EFermi-\Evalence}{\kB T} > 3.6$}{}
|
||||
\eq{
|
||||
n_0 &\approx N_\text{c}(T) \Exp{-\frac{E_\text{c} - \EFermi}{\kB T}} \\
|
||||
p_0 &\approx N_\text{v}(T) \Exp{-\frac{\EFermi - E_\text{v}}{\kB T}}
|
||||
\ger{
|
||||
Intrirnsisch: Pur, Elektronendichte gegeben durch thermische Anregung und $n_i^2 = n_0 p_0$ \\
|
||||
Extrinsisch: gedoped
|
||||
}
|
||||
\end{formula}
|
||||
\begin{formula}{charge_density_intrinsic}
|
||||
\desc{Intrinsic charge density}{}{}
|
||||
\desc[german]{Intrinsische Ladungsträgerdichte}{}{}
|
||||
\eq{
|
||||
n_\text{i} \approx \sqrt{n_0 p_0} = \sqrt{N_\text{c}(T) N_\text{v}(T)} \Exp{-\frac{E_\text{gap}}{2\kB T}}
|
||||
}
|
||||
\end{formula}
|
||||
}
|
||||
\end{formula}
|
||||
|
||||
\begin{formula}{mass_action}
|
||||
\desc{Mass action law}{Charge densities at thermal equilibrium, independent of doping}{}
|
||||
\desc[german]{Massenwirkungsgesetz}{Ladungsträgerdichten im Equilibrium, unabhängig der Dotierung }{}
|
||||
\eq{np = n_i^2}
|
||||
\end{formula}
|
||||
\begin{formula}{charge_density_eq}
|
||||
\desc{Equilibrium charge densitites}{Holds when $\frac{\Econd-\EFermi}{\kB T}>3.6$ and $\frac{\EFermi-\Evalence}{\kB T} > 3.6$}{}
|
||||
\desc[german]{Ladungsträgerdichte im Equilibrium}{Gilt wenn $\frac{\Econd-\EFermi}{\kB T}>3.6$ und $\frac{\EFermi-\Evalence}{\kB T} > 3.6$}{}
|
||||
\eq{
|
||||
n_0 &\approx N_\text{c}(T) \Exp{-\frac{E_\text{c} - \EFermi}{\kB T}} \\
|
||||
p_0 &\approx N_\text{v}(T) \Exp{-\frac{\EFermi - E_\text{v}}{\kB T}}
|
||||
}
|
||||
\end{formula}
|
||||
\begin{formula}{charge_density_intrinsic}
|
||||
\desc{Intrinsic charge density}{}{}
|
||||
\desc[german]{Intrinsische Ladungsträgerdichte}{}{}
|
||||
\eq{
|
||||
n_\text{i} \approx \sqrt{n_0 p_0} = \sqrt{N_\text{c}(T) N_\text{v}(T)} \Exp{-\frac{E_\text{gap}}{2\kB T}}
|
||||
}
|
||||
\end{formula}
|
||||
|
||||
|
||||
\begin{formula}{mass_action}
|
||||
\desc{Mass action law}{Charge densities at thermal equilibrium, independent of doping}{}
|
||||
\desc[german]{Massenwirkungsgesetz}{Ladungsträgerdichten im Equilibrium, unabhängig der Dotierung }{}
|
||||
\eq{np = n_i^2}
|
||||
\end{formula}
|
||||
|
||||
|
||||
\begin{formula}{bandgaps}
|
||||
\desc{Bandgaps of common semiconductors}{}{}
|
||||
\desc[german]{Bandlücken wichtiger Halbleiter}{}{}
|
||||
\begin{tabular}{l|CCc}
|
||||
& \Egap(\SI{0}{\kelvin}) [\si{\eV}] & \Egap(\SI{300}{\kelvin}) [\si{\eV}] & \\ \hline
|
||||
\GT{diamond} & 5,48 & 5,47 & \GT{indirect} \\
|
||||
@ -51,23 +54,107 @@
|
||||
InP & 1,42 & 1,35 & \GT{direct} \\
|
||||
CdS & 2.58 & 2.42 & \GT{direct}
|
||||
\end{tabular}
|
||||
\end{formula}
|
||||
|
||||
\begin{formula}{min_maj}
|
||||
\desc{Minority / Majority charge carriers}{}{}
|
||||
\desc[german]{Minoritäts- / Majoritätsladungstraäger}{}{}
|
||||
|
||||
\begin{formula}{min_maj}
|
||||
\desc{Minority / Majority charge carriers}{}{}
|
||||
\desc[german]{Minoritäts- / Majoritätsladungstraäger}{}{}
|
||||
\ttxt{
|
||||
\eng{
|
||||
Majority carriers: higher number of particles ($e^-$ in n-type, $h^+$ in p-type)\\
|
||||
Minority carriers: lower number of particles ($h^+$ in n-type, $e^-$ in p-type)
|
||||
}
|
||||
\ger{
|
||||
Majoritätsladungstraäger: höhere Teilchenzahl ($e^-$ in n-Typ, $h^+$ in p-Typ)\\
|
||||
Minoritätsladungsträger: niedrigere Teilchenzahl ($h^+$ in n-Typ, $e^-$ in p-Typ)
|
||||
}
|
||||
}
|
||||
\end{formula}
|
||||
\TODO{effective mass approx}
|
||||
|
||||
|
||||
\Subsection[
|
||||
\eng{Devices and junctions}
|
||||
\ger{Bauelemente und Kontakte}
|
||||
]{junctions}
|
||||
\begin{formula}{metal-sc}
|
||||
\desc{Metal-semiconductor junction}{}{}
|
||||
\desc[german]{Metall-Halbleiter Kontakt}{}{}
|
||||
% \ttxt{
|
||||
% \eng{
|
||||
|
||||
% }
|
||||
% }
|
||||
\end{formula}
|
||||
|
||||
\begin{bigformula}{schottky_barrier}
|
||||
\desc{Schottky barrier}{Rectifying \fqEqRef{cm:sc:junctions:metal-sc}}{}
|
||||
% \desc[german]{}{}{}
|
||||
\centering
|
||||
\resizebox{0.49\textwidth}{!}{\input{img/cm/sc_junction_metal_n_sc_separate.tex}}
|
||||
\resizebox{0.49\textwidth}{!}{\input{img/cm/sc_junction_metal_n_sc.tex}}
|
||||
\TODO{Work function electron affinity sind doch Energien und keine Potentiale, warum wird also immer $q$ davor geschrieben?}
|
||||
\end{bigformula}
|
||||
\begin{formula}{schottky-mott_rule}
|
||||
\desc{Schottky-Mott rule}{}{$\Phi_\txB$ barrier potential, $\Phi_\txM$ \GT{metal} \qtyRef{work_function}, $\chi_\text{sc}$ \qtyRef{electron_affinity}}
|
||||
% \desc[german]{}{}{}
|
||||
\eq{\Phi_\txB \approx \Phi_\txM - \chi_\text{sc}}
|
||||
\end{formula}
|
||||
\TODO{work function verhältnisse, wann ist es ohmisch wann depleted?}
|
||||
\begin{bigformula}{ohmic}
|
||||
\desc{Ohmic contact}{}{}
|
||||
\desc[german]{Ohmscher Kontakt}{}{}
|
||||
\centering
|
||||
\resizebox{0.49\textwidth}{!}{\input{img/cm/sc_junction_ohmic_separate.tex}}
|
||||
\resizebox{0.49\textwidth}{!}{\input{img/cm/sc_junction_ohmic.tex}}
|
||||
\end{bigformula}
|
||||
|
||||
\begin{bigformula}{pn}
|
||||
\desc{p-n junction}{}{}
|
||||
\desc[german]{p-n Übergang}{}{}
|
||||
\centering
|
||||
\input{img/cm/sc_junction_pn.tex}
|
||||
\resizebox{0.49\textwidth}{!}{\tikzPnJunction{1/3}{0}{0}{1/3}{0}{0}{}}
|
||||
\resizebox{0.49\textwidth}{!}{\tikzPnJunction{1/2}{0.4}{-0.4}{1/2}{-0.4}{0.4}{}}
|
||||
\end{bigformula}
|
||||
|
||||
|
||||
|
||||
\Subsection[
|
||||
\eng{Excitons}
|
||||
\ger{Exzitons}
|
||||
]{exciton}
|
||||
\begin{formula}{desc}
|
||||
\desc{Exciton}{}{}
|
||||
\desc[german]{Exziton}{}{}
|
||||
\ttxt{
|
||||
\eng{
|
||||
Majority carriers: higher number of particles ($e^-$ in n-type, $h^+$ in p-type)\\
|
||||
Minority carriers: lower number of particles ($h^+$ in n-type, $e^-$ in p-type)
|
||||
Quasi particle, excitation in condensed matter as bound electron-hole pair.
|
||||
\\ Free (Wannier) excitons: delocalised over many lattice sites
|
||||
\\ Bound (Frenkel) excitonsi: localised in single unit cell
|
||||
}
|
||||
|
||||
\ger{
|
||||
Majoritätsladungstraäger: höhere Teilchenzahl ($e^-$ in n-Typ, $h^+$ in p-Typ)\\
|
||||
Minoritätsladungsträger: niedrigere Teilchenzahl ($h^+$ in n-Typ, $e^-$ in p-Typ)
|
||||
Quasiteilchen, Anregung im Festkörper als gebundenes Elektron-Loch-Paar
|
||||
\\ Freie (Wannier) Exzitons: delokalisiert, über mehrere Einheitszellen
|
||||
\\ Gebundene (Frenkel) Exzitons: lokalisiert in einer Einheitszelle
|
||||
}
|
||||
}
|
||||
\end{formula}
|
||||
|
||||
|
||||
|
||||
|
||||
|
||||
\end{formula}
|
||||
\eng[free_X]{for free Excitons}
|
||||
\ger[free_X]{für freie Exzitons}
|
||||
\begin{formula}{rydberg}
|
||||
\desc{Exciton Rydberg energy}{\gt{free_X}}{$R_\txH$ \fqEqRef{qm:h:rydberg_energy}}
|
||||
\desc[german]{}{}{}
|
||||
\eq{
|
||||
E(n) = - \left(\frac{\mu}{m_0\epsilon_r^2}\right) R_\txH \frac{1}{n^2}
|
||||
}
|
||||
\end{formula}
|
||||
\begin{formula}{bohr_radius}
|
||||
\desc{Exciton Bohr radius}{\gt{free_X}}{\QtyRef{relative_permittivity}, \ConstRef{bohr_radius}, \ConstRef{electron_mass}, $mu$ \GT{reduced_mass}}
|
||||
\desc[german]{Exziton-Bohr Radius}{}{}
|
||||
\eq{
|
||||
r_n = \left(\frac{m_\txe\epsilon_r a_\txB}{mu}\right) n^2
|
||||
}
|
||||
\end{formula}
|
||||
|
||||
@ -2,10 +2,71 @@
|
||||
\eng{Measurement techniques}
|
||||
\ger{Messtechniken}
|
||||
]{meas}
|
||||
|
||||
\newcommand\newTechnique{\hline}
|
||||
\Eng[name]{Name}
|
||||
\Ger[name]{Name}
|
||||
\Eng[application]{Application}
|
||||
\Ger[application]{Anwendung}
|
||||
|
||||
\Subsection[
|
||||
\eng{Raman spectroscopy}
|
||||
\ger{Raman Spektroskopie}
|
||||
]{raman}
|
||||
% \begin{minipagetable}{raman}
|
||||
% \entry{name}{
|
||||
% \eng{Raman spectroscopy}
|
||||
% \ger{Raman-Spektroskopie}
|
||||
% }
|
||||
% \entry{application}{
|
||||
% \eng{Vibrational modes, Crystal structure, Doping, Band Gaps, Layer thickness in \fqEqName{cm:misc:vdw_material}}
|
||||
% \ger{Vibrationsmoden, Kristallstruktur, Dotierung, Bandlücke, Schichtdicke im \fqEqName{cm:misc:vdw_material}}
|
||||
% }
|
||||
% % \entry{how}{
|
||||
% % \eng{Monochromatic light (\fqEqRef{Laser}) shines on sample, inelastic scattering because of rotation-, vibration-, phonon and spinflip-processes, plot spectrum as shift of the laser light (in \si{\per\cm})}
|
||||
% % \ger{Monochromatisches Licht (\fqEqRef{Laser}) bestrahlt Probe, inelastische Streuung durch Rotations-, Schwingungs-, Phonon und Spin-Flip-Prozesse, plotte Spektrum als Verschiebung gegen das Laser Licht (in \si{\per\cm}) }
|
||||
% % }
|
||||
% \end{minipagetable}
|
||||
\begin{minipage}{0.5\textwidth}
|
||||
\begin{figure}[H]
|
||||
\centering
|
||||
% \includegraphics[width=0.8\textwidth]{img/cm_amf.pdf}
|
||||
% \caption{\cite{Bian2021}}
|
||||
\end{figure}
|
||||
\end{minipage}
|
||||
|
||||
\expandafter\detokenize\expandafter{\fqname}
|
||||
\GT{cm:meas:raman:raman:application}
|
||||
|
||||
\separateEntries
|
||||
|
||||
% \begin{minipagetable}{pl}
|
||||
% \entry{name}{
|
||||
% \eng{Photoluminescence spectroscopy}
|
||||
% \ger{Photolumeszenz-Spektroskopie}
|
||||
% }
|
||||
% \entry{application}{
|
||||
% \eng{Crystal structure, Doping, Band Gaps, Layer thickness in \fqEqName{cm:misc:vdw_material}}
|
||||
% \ger{Kristallstruktur, Dotierung, Bandlücke, Schichtdicke im \fqEqName{cm:misc:vdw_material}}
|
||||
% }
|
||||
% \entry{how}{
|
||||
% \eng{Monochromatic light (\fqEqRef{Laser}) shines on sample, electrons are excited, relax to the conduction band minimum and finally accross the band gap under photon emission}
|
||||
% \ger{Monochromatisches Licht (\fqEqRef{Laser}) bestrahlt Probe, Elektronen werden angeregt und relaxieren in das Leitungsband-Minimum und schließlich über die Bandlücke unter Photonemission}
|
||||
% }
|
||||
% \end{minipagetable}
|
||||
\begin{minipage}{0.5\textwidth}
|
||||
\begin{figure}[H]
|
||||
\centering
|
||||
% \includegraphics[width=0.8\textwidth]{img/cm_amf.pdf}
|
||||
% \caption{\cite{Bian2021}}
|
||||
\end{figure}
|
||||
\end{minipage}
|
||||
|
||||
|
||||
\Subsection[
|
||||
\eng{ARPES}
|
||||
\ger{ARPES}
|
||||
]{arpes}
|
||||
]{arpes}
|
||||
what?
|
||||
in?
|
||||
how?
|
||||
@ -20,11 +81,6 @@
|
||||
\ger{Bilder der Oberfläche einer Probe werden erstellt, indem die Probe mit einer Sonde abgetastet wird.}
|
||||
\end{ttext}
|
||||
|
||||
\Eng[name]{Name}
|
||||
\Ger[name]{Name}
|
||||
\Eng[application]{Application}
|
||||
\Ger[application]{Anwendung}
|
||||
|
||||
|
||||
\begin{minipagetable}{amf}
|
||||
\entry{name}{
|
||||
@ -49,6 +105,8 @@
|
||||
\end{minipage}
|
||||
|
||||
|
||||
|
||||
|
||||
\begin{minipagetable}{stm}
|
||||
\entry{name}{
|
||||
\eng{Scanning tunneling microscopy (STM)}
|
||||
|
||||
@ -1,8 +1,8 @@
|
||||
\Part[
|
||||
\Section[
|
||||
\eng{Topological Materials}
|
||||
\ger{Topologische Materialien}
|
||||
]{topo}
|
||||
\Section[
|
||||
\Subsection[
|
||||
\eng{Berry phase / Geometric phase}
|
||||
\ger{Berry-Phase / Geometrische Phase}
|
||||
]{berry_phase}
|
||||
87
src/comp/ad.tex
Normal file
87
src/comp/ad.tex
Normal file
@ -0,0 +1,87 @@
|
||||
\Section[
|
||||
\eng{Atomic dynamics}
|
||||
% \ger{}
|
||||
]{ad}
|
||||
\Subsection[
|
||||
\eng{Born-Oppenheimer Approximation}
|
||||
\ger{Born-Oppenheimer Näherung}
|
||||
]{bo}
|
||||
\begin{formula}{hamiltonian}
|
||||
\desc{Electron Hamiltonian}{}{$\hat{T}$ \fqEqRef{comp:elsth:kinetic_energy}, $\hat{V}$ \fqEqRef{comp:elsth:potential_energy}, $\txe$ \GT{electrons}, $\txn$ \GT{nucleons}}
|
||||
\desc[german]{Hamiltonian der Elektronen}{}{}
|
||||
\eq{\hat{H}_\txe = \hat{T}_\txe + V_{\txe \leftrightarrow \txe} + V_{\txn \leftrightarrow \txe}}
|
||||
\end{formula}
|
||||
\begin{formula}{ansatz}
|
||||
\desc{Wave function ansatz}{}{$\psi_\text{en}^n$ eigenstate $n$ of \fqEqRef{comp:elst:hamiltonian}, $\psi_\txe^i$ eigenstate $i$ of \fqEqRef{comp:ad:bo:hamiltonian}, $\vecr,\vecR$ electron/nucleus positions, $\sigma$ electron spin, $c^{ni}$ coefficients}
|
||||
\desc[german]{Wellenfunktion Ansatz}{}{}
|
||||
\eq{\psi_\text{en}^n\big(\{\vecr,\sigma\},\{\vecR\}\big) = \sum_i c^{ni}\big(\{\vecR\}\big)\, \psi_\txe^i\big(\{\vecr,\sigma\},\{\vecR\}\big)}
|
||||
\end{formula}
|
||||
\begin{formula}{equation}
|
||||
\desc{Equation}{}{}
|
||||
% \desc[german]{}{}{}
|
||||
\eq{
|
||||
\label{eq:\fqname}
|
||||
\left[E_\txe^j\big(\{\vecR\}\big) + \hat{T}_\txn + V_{\txn \leftrightarrow \txn} - E^n \right]c^{nj} = -\sum_i \Lambda_{ij} c^{ni}\big(\{\vecR\}\big)
|
||||
}
|
||||
\end{formula}
|
||||
\begin{formula}{coupling_operator}
|
||||
\desc{Exact nonadiabtic coupling operator}{Electron-phonon couplings / electron-vibrational couplings}{$\psi^i_\txe$ electronic states, $\vecR$ nucleus position, $M$ nucleus \qtyRef{mass}}
|
||||
% \desc[german]{}{}{}
|
||||
\begin{multline}
|
||||
\Lambda_{ij} = \int \d^3r (\psi_\txe^j)^* \left(-\sum_I \frac{\hbar^2\nabla_{\vecR_I}^2}{2M_I}\right) \psi_\txe^i \\
|
||||
+ \sum_I \frac{1}{M_I} \int\d^3r \left[(\psi_\txe^j)^* (-i\hbar\nabla_{\vecR_I})\psi_\txe^i\right](-i\hbar\nabla_{\vecR_I})
|
||||
\end{multline}
|
||||
\end{formula}
|
||||
\begin{formula}{adiabatic_approx}
|
||||
\desc{Adiabatic approximation}{Electronic configuration remains the same when atoms move}{$\Lambda_{ij}$ \fqEqRef{comp:ad:bo:coupling_operator}}
|
||||
\desc[german]{Adiabatische Näherung}{Elektronenkonfiguration bleibt gleich bei Bewegung der Atome gleich}{}
|
||||
\eq{\Lambda_{ij} = 0 \quad \text{\GT{for} } i\neq j}
|
||||
\end{formula}
|
||||
\begin{formula}{approx}
|
||||
\desc{Born-Oppenheimer approximation}{}{\GT{see} \fqEqRef{comp:ad:bo:equation}}
|
||||
\desc[german]{Born-Oppenheimer Näherung}{}{}
|
||||
\begin{gather}
|
||||
\Lambda_{ij} = 0
|
||||
\shortintertext{\fqEqRef{comp:ad:bo:equation} \Rightarrow}
|
||||
\left[E_e^i\big(\{\vecR\}\big) + \hat{T}_\txn - E^n\right]c^{ni}\big(\{\vecR\}\big) = 0
|
||||
\end{gather}
|
||||
\end{formula}
|
||||
|
||||
\begin{formula}{surface}
|
||||
\desc{Born-Oppenheimer surface}{Potential energy surface (PES)\\ The nuclei follow Newtons equations of motion on the BO surface if the system is in the electronic ground state}{$E_\txe^0, \psi_\txe^0$ lowest eigenvalue/eigenstate of \fqEqRef{comp:ad:bo:hamiltonian}}
|
||||
\desc[german]{Born-Oppenheimer Potentialhyperfläche}{Die Nukleonen Newtons klassichen Bewegungsgleichungen auf der BO Hyperfläche wenn das System im elektronischen Grundzustand ist}{$E_\txe^0, \psi_\txe^0$ niedrigster Eigenwert/Eigenzustand vom \fqEqRef{comp:ad:bo:hamiltonian}}
|
||||
\begin{gather}
|
||||
V_\text{BO}\big(\{\vecR\}\big) = E_\txe^0\big(\{\vecR\}\big) \\
|
||||
M_I \ddot{\vecR}_I(t) = - \Grad_{\vecR_I} V_\text{BO}\big(\{\vecR(t)\}\big)
|
||||
\shortintertext{\GT{ansatz} \GT{for} \fqEqRef{comp:ad:bo:approx}}
|
||||
\psi_\text{BO} = c^{n0} \big(\{\vecR\}\big) \,\psi_\txe^0 \big(\{\vecr,\sigma\},\{\vecR\}\big)
|
||||
\end{gather}
|
||||
\end{formula}
|
||||
|
||||
\begin{formula}{limitations}
|
||||
\desc{Limitations}{}{}
|
||||
\desc[german]{Limitationen}{}{}
|
||||
\ttxt{
|
||||
\eng{
|
||||
\begin{itemize}
|
||||
\item Nuclei velocities must be small and electron energy state differences large
|
||||
\item Nuclei need spin for effects like spin-orbit coupling
|
||||
\item Nonadiabitc effects in photochemistry, proteins
|
||||
\end{itemize}
|
||||
}
|
||||
}
|
||||
\end{formula}
|
||||
\TODO{geometry optization?, lattice vibrations (harmionic approx, dynamical matrix)}
|
||||
|
||||
|
||||
\Subsection[
|
||||
\eng{Molecular Dynamics}
|
||||
\ger{Molekulardynamik}
|
||||
]{md}
|
||||
\begin{ttext}
|
||||
\eng{Statistical method}
|
||||
|
||||
\end{ttext}
|
||||
|
||||
\TODO{ab-initio MD, force-field MD}
|
||||
|
||||
4
src/comp/comp.tex
Normal file
4
src/comp/comp.tex
Normal file
@ -0,0 +1,4 @@
|
||||
\Part[
|
||||
\eng{Computational Physics}
|
||||
\ger{Computergestützte Physik}
|
||||
]{comp}
|
||||
183
src/comp/elsth.tex
Normal file
183
src/comp/elsth.tex
Normal file
@ -0,0 +1,183 @@
|
||||
\Section[
|
||||
\eng{Electronic structure theory}
|
||||
% \ger{}
|
||||
]{elst}
|
||||
\begin{formula}{kinetic_energy}
|
||||
\desc{Kinetic energy}{of species $i$}{$i$ = nucleons/electrons, $N$ number of particles, $m$ \qtyRef{mass}}
|
||||
\desc[german]{Kinetische Energie}{von Spezies $i$}{$i$ = Nukleonen/Elektronen, $N$ Teilchenzahl, $m$ \qtyRef{mass}}
|
||||
\eq{\hat{T}_i &= -\sum_{n=1}^{N_i} \frac{\hbar^2}{2 m_i} \vec{\nabla}^2_n}
|
||||
\end{formula}
|
||||
\begin{formula}{potential_energy}
|
||||
\desc{Electrostatic potential}{between species $i$ and $j$}{$i,j$ = nucleons/electrons, $r$ particle position, $Z_i$ charge of species $i$, \ConstRef{charge}}
|
||||
\desc[german]{Elektrostatisches Potential}{zwischen Spezies $i$ und $j$}{}
|
||||
\eq{\hat{V}_{i \leftrightarrow j} &= -\sum_{k,l} \frac{Z_i Z_j e^2}{\abs{\vecr_k - \vecr_l}}}
|
||||
\end{formula}
|
||||
\begin{formula}{hamiltonian}
|
||||
\desc{Electronic structure Hamiltonian}{}{$\hat{T}$ \fqEqRef{comp:elsth:kinetic_energy}, $\hat{V}$ \fqEqRef{comp:elsth:potential_energy}, $\txe$ \GT{electrons}, $\txn$ \GT{nucleons}}
|
||||
\eq{\hat{H} &= \hat{T}_\txe + \hat{T}_\txn + V_{\txe \leftrightarrow \txe} + V_{\txn \leftrightarrow \txe} + V_{\txn \leftrightarrow \txn}}
|
||||
\end{formula}
|
||||
\begin{formula}{mean_field}
|
||||
\desc{Mean field approximation}{Replaces 2-particle operator by 1-particle operator}{Example for Coulumb interaction between many electrons}
|
||||
\desc[german]{Molekularfeldnäherung}{Ersetzt 2-Teilchen Operator durch 1-Teilchen Operator}{Beispiel für Coulumb Wechselwirkung zwischen Elektronen}
|
||||
\eq{
|
||||
\frac{1}{2}\sum_{i\neq j} \frac{e^2}{\abs{\vec{r}_i - \vec{r}_j}} \approx \sum_{i} V_\text{eff}(\vec{r}_i)
|
||||
}
|
||||
\end{formula}
|
||||
|
||||
|
||||
\Subsection[
|
||||
\eng{Tight-binding}
|
||||
\ger{Modell der stark gebundenen Elektronen / Tight-binding}
|
||||
]{tb}
|
||||
\begin{formula}{assumptions}
|
||||
\desc{Assumptions}{}{}
|
||||
\desc[german]{Annahmen}{}{}
|
||||
\ttxt{
|
||||
\eng{
|
||||
\begin{itemize}
|
||||
\item Atomic wave functions are localized \Rightarrow Small overlap, interaction cutoff
|
||||
\end{itemize}
|
||||
}
|
||||
}
|
||||
\end{formula}
|
||||
\begin{formula}{hamiltonian}
|
||||
\desc{Tight-binding Hamiltonian}{in second quantized form}{$\hat{a}_i^\dagger$, $\hat{a}_i$ \GT{creation_annihilation_ops} create/destory an electron on site $i$, $\epsilon_i$ on-site energy, $t_{i,j}$ hopping amplitude, usually $\epsilon$ and $t$ are determined from experiments or other methods}
|
||||
\desc[german]{Tight-binding Hamiltonian}{in zweiter Quantisierung}{$\hat{a}_i^\dagger$, $\hat{a}_i$ \GT{creation_annihilation_ops} erzeugen/vernichten ein Elektron auf Platz $i$, $\epsilon_i$ on-site Energie, $t_{i,j}$ hopping Amplitude, meist werden $\epsilon$ und $t$ aus experimentellen Daten oder anderen Methoden bestimmt}
|
||||
\eq{\hat{H} = \sum_i \epsilon_i \hat{a}_i^\dagger \hat{a}_i - \sum_{i,j} t_{i,j} \left(\hat{a}_i^\dagger \hat{a}_j + \hat{a}_j^\dagger \hat{a}_i\right)}
|
||||
\end{formula}
|
||||
|
||||
|
||||
|
||||
\Subsection[
|
||||
\eng{Density functional theory (DFT)}
|
||||
\ger{Dichtefunktionaltheorie (DFT)}
|
||||
]{dft}
|
||||
\Subsubsection[
|
||||
\eng{Hartree-Fock}
|
||||
\ger{Hartree-Fock}
|
||||
]{hf}
|
||||
\begin{formula}{description}
|
||||
\desc{Description}{}{}
|
||||
\desc[german]{Beschreibung}{}{}
|
||||
\begin{ttext}
|
||||
\eng{
|
||||
\begin{itemize}
|
||||
\item \fqEqRef{comp:elst:mean_field} theory obeying the Pauli principle
|
||||
\item Self-interaction free: Self interaction is cancelled out by the Fock-term
|
||||
\end{itemize}
|
||||
}
|
||||
\end{ttext}
|
||||
\end{formula}
|
||||
\begin{formula}{equation}
|
||||
\desc{Hartree-Fock equation}{}{
|
||||
$\varphi_\xi$ single particle wavefunction of $\xi$th orbital,
|
||||
$\hat{T}$ kinetic electron energy,
|
||||
$\hat{V}_{\text{en}}$ electron-nucleus attraction,
|
||||
$\hat{V}_{\text{HF}}$ \fqEqRef{comp:dft:hf:potential},
|
||||
}
|
||||
\desc[german]{Hartree-Fock Gleichung}{}{
|
||||
$\varphi_\xi$ ein-Teilchen Wellenfunktion des $\xi$-ten Orbitals,
|
||||
$\hat{T}$ kinetische Energie der Elektronen,
|
||||
$\hat{V}_{\text{en}}$ Electron-Kern Anziehung,
|
||||
$\hat{V}_{\text{HF}}$ \fqEqRef{comp:dft:hf:potential}
|
||||
}
|
||||
\eq{
|
||||
\left(\hat{T} + \hat{V}_{\text{en}} + \hat{V}_{\text{HF}}^\xi\right)\varphi_\xi(x) = \epsilon_\xi \varphi_\xi(x)
|
||||
}
|
||||
\end{formula}
|
||||
\begin{formula}{potential}
|
||||
\desc{Hartree-Fock potential}{}{}
|
||||
\desc[german]{Hartree Fock Potential}{}{}
|
||||
\eq{
|
||||
V_{\text{HF}}^\xi(\vecr) =
|
||||
\sum_{\vartheta} \int \d x'
|
||||
\frac{e^2}{\abs{\vecr - \vecr'}}
|
||||
\left(
|
||||
\underbrace{\abs{\varphi_\xi(x')}^2}_{\text{Hartree-Term}}
|
||||
- \underbrace{\frac{\varphi_{\vartheta}^*(x') \varphi_{\xi}(x') \varphi_{\vartheta}(x)}{\varphi_\xi(x)}}_{\text{Fock-Term}}
|
||||
\right)
|
||||
}
|
||||
\end{formula}
|
||||
\begin{formula}{scf}
|
||||
\desc{Self-consistent field cycle}{}{}
|
||||
% \desc[german]{}{}{}
|
||||
\ttxt{
|
||||
\eng{
|
||||
\begin{enumerate}
|
||||
\item Initial guess for $\psi$
|
||||
\item Solve SG for each particle
|
||||
\item Make new guess for $\psi$
|
||||
\end{enumerate}
|
||||
}
|
||||
}
|
||||
\end{formula}
|
||||
|
||||
\Subsubsection[
|
||||
\eng{Hohenberg-Kohn Theorems}
|
||||
\ger{Hohenberg-Kohn Theoreme}
|
||||
]{hk}
|
||||
\begin{formula}{hk1}
|
||||
\desc{Hohenberg-Kohn theorem (HK1)}{}{}
|
||||
\desc[german]{Hohenberg-Kohn Theorem (HK1)}{}{}
|
||||
\ttxt{
|
||||
\eng{For any system of interacting electrons, the ground state electron density $n(\vecr)$ determines $\hat{V}_\text{ext}$ uniquely up to a trivial constant. }
|
||||
\ger{Die Elektronendichte des Grundzustandes $n(\vecr)$ bestimmt ein einzigartiges $\hat{V}_{\text{ext}}$ eines Systems aus interagierenden Elektronen bis auf eine Konstante.}
|
||||
}
|
||||
\end{formula}
|
||||
\begin{formula}{hk2}
|
||||
\desc{Hohenberg-Kohn theorem (HK2)}{}{}
|
||||
\desc[german]{Hohenberg-Kohn Theorem (HK2)}{}{}
|
||||
\ttxt{
|
||||
\eng{Given the energy functional $E[n(\vecr)]$, the ground state density and energy can be obtained variationally. The density that minimizes the total energy is the ecxact ground state density. }
|
||||
\ger{Für ein Energiefunktional $E[n(\vecr)]$ kann die Grundzustandsdichte und Energie durch systematische Variation bestimmt werden. Die Dichte, welche die Gesamtenergie minimiert ist die exakte Grundzustandsichte. }
|
||||
}
|
||||
\end{formula}
|
||||
|
||||
\Subsubsection[
|
||||
\eng{Kohn-Sham DFT}
|
||||
\ger{Kohn-Sham DFT}
|
||||
]{ks}
|
||||
\begin{formula}{map}
|
||||
\desc{Kohn-Sham map}{}{}
|
||||
\desc[german]{Kohn-Sham Map}{}{}
|
||||
\ttxt{
|
||||
\eng{Maps fully interacting system of electrons to a system of non-interacting electrons with the same ground state density $n^\prime(\vecr) = n(\vecr)$}
|
||||
}
|
||||
\eq{n(\vecr) = \sum_{i=1}^N \abs{\phi_i(\vecr)}^2}
|
||||
\end{formula}
|
||||
\begin{formula}{functional}
|
||||
\desc{Kohn-Sham functional}{}{$T_\text{KS}$ kinetic enery, $V_\text{ext}$ external potential, $E_\txH$ \hyperref[f:comp:elst:dft:hf:potential]{Hartree term}, $E_\text{XC}$ exchange correlation functional}
|
||||
\desc[german]{Kohn-Sham Funktional}{}{}
|
||||
\eq{E_\text{KS}[n(\vecr)] = T_\text{KS}[n(\vecr)] + V_\text{ext}[n(\vecr)] + E_\text{H}[n(\vecr)] + E_\text{XC}[n(\vecr)] }
|
||||
\end{formula}
|
||||
|
||||
\begin{formula}{equation}
|
||||
\desc{Kohn-Sham equation}{Solving it uses up a large portion of supercomputer resources}{$\phi_i^\text{KS}$ KS orbitals}
|
||||
\desc[german]{Kohn-Sham Gleichung}{Die Lösung der Gleichung macht einen großen Teil der Supercomputer Ressourcen aus}{}
|
||||
\begin{multline}
|
||||
\biggr\{
|
||||
-\frac{\hbar^2\nabla^2}{2m}
|
||||
+ v_\text{ext}(\vecr)
|
||||
+ e^2 \int\d^3 \vecr^\prime \frac{n(\vecr^\prime)}{\abs{\vecr-\vecr^\prime}} \\
|
||||
+ \pdv{E_\txX[n(\vecr)]}{n(\vecr)}
|
||||
+ \pdv{E_\txC[n(\vecr)]}{n(\vecr)}
|
||||
\biggr\} \phi_i^\text{KS}(\vecr) =\\
|
||||
= \epsilon_i^\text{KS} \phi_i^\text{KS}(\vecr)
|
||||
\end{multline}
|
||||
\end{formula}
|
||||
\begin{formula}{scf}
|
||||
\desc{Self-consistent field cycle for Kohn-Sham}{}{}
|
||||
% \desc[german]{}{}{}
|
||||
\ttxt{
|
||||
\itemsep=\parsep
|
||||
\eng{
|
||||
\begin{enumerate}
|
||||
\item Initial guess for $n(\vecr)$
|
||||
\item Calculate effective potential $V_\text{eff}$
|
||||
\item Solve \fqEqRef{comp:elst:dft:ks:equation}
|
||||
\item Calculate density $n(\vecr)$
|
||||
\item Repeat 2-4 until self consistent
|
||||
\end{enumerate}
|
||||
}
|
||||
}
|
||||
\end{formula}
|
||||
84
src/comp/ml.tex
Normal file
84
src/comp/ml.tex
Normal file
@ -0,0 +1,84 @@
|
||||
\Section[
|
||||
\eng{Machine-Learning}
|
||||
\ger{Maschinelles Lernen}
|
||||
]{ml}
|
||||
\Subsection[
|
||||
\eng{Performance metrics}
|
||||
\ger{Metriken zur Leistungsmessung}
|
||||
]{performance}
|
||||
\eng[cp]{correct predictions}
|
||||
\ger[cp]{richtige Vorhersagen}
|
||||
\eng[fp]{false predictions}
|
||||
\ger[fp]{falsche Vorhersagen}
|
||||
|
||||
\eng[y]{ground truth}
|
||||
\eng[yhat]{prediction}
|
||||
\ger[y]{Wahrheit}
|
||||
\ger[yhat]{Vorhersage}
|
||||
|
||||
\begin{formula}{accuracy}
|
||||
\desc{Accuracy}{}{}
|
||||
\desc[german]{Genauigkeit}{}{}
|
||||
\eq{a = \frac{\tgt{cp}}{\tgt{fp} + \tgt{cp}}}
|
||||
\end{formula}
|
||||
\TODO{is $n$ the nuber of predictions or the number of output features?}
|
||||
\begin{formula}{mean_abs_error}
|
||||
\desc{Mean absolute error (MAE)}{}{$y$ \gt{y}, $\hat{y}$ \gt{yhat}, $n$ ?}
|
||||
\desc[german]{Mittlerer absoluter Fehler (MAE)}{}{}
|
||||
\eq{\text{MAE} = \frac{1}{n} \sum_{i=1}^n \abs{y_i - \hat{y}_i}}
|
||||
\end{formula}
|
||||
\begin{formula}{root_mean_square_error}
|
||||
\desc{Root mean squared error (RMSE)}{}{$y$ \gt{y}, $\hat{y}$ \gt{yhat}, $n$ ?}
|
||||
\desc[german]{Standardfehler der Regression}{Quadratwurzel des mittleren quadratischen Fehlers (RSME)}{}
|
||||
\eq{\text{RMSE} = \sqrt{\frac{1}{n} \sum_{i=1}^n \left(y_i - \hat{y}_i\right)^2}}
|
||||
\end{formula}
|
||||
|
||||
\Subsection[
|
||||
\eng{Regression}
|
||||
\ger{Regression}
|
||||
]{reg}
|
||||
\Subsubsection[
|
||||
\eng{Linear Regression}
|
||||
\ger{Lineare Regression}
|
||||
]{linear}
|
||||
\begin{formula}{eq}
|
||||
\desc{Linear regression}{Fits the data under the assumption of \hyperref[f:math:pt:distributions:cont:normal]{normally distributed errors}}{$\mat{x}\in\R^{N\times M}$ input data, $\mat{y}\in\R^{N\times L}$ output data, $\mat{b}$ bias, $\vec{W}$ weights, $N$ samples, $M$ features, $L$ output variables}
|
||||
\desc[german]{Lineare Regression}{Fitted Daten unter der Annahme \hyperref[f:math:pt:distributions:cont:normal]{normalverteilter Fehler}}{}
|
||||
\eq{\mat{y} = \mat{b} + \mat{x} \cdot \vec{W}}
|
||||
\end{formula}
|
||||
\begin{formula}{design_matrix}
|
||||
\desc{Design matrix}{Stack column of ones to the feature vector\\Useful when $b$ is scalar}{$x_{ij}$ feature $j$ of sample $i$}
|
||||
\desc[german]{Designmatrix Ansatz}{}{}
|
||||
\eq{
|
||||
\mat{X} = \begin{pmatrix} 1 & x_{11} & \ldots & x_{1M} \\ \vdots & \vdots & \vdots & \vdots \\ 1 & x_{N1} & \ldots & x_{NM} \end{pmatrix}
|
||||
}
|
||||
\end{formula}
|
||||
\begin{formula}{scalar_bias}
|
||||
\desc{Linear regression with scalar bias}{Using the design matrix, the scalar is absorbed into the weight vector}{$\mat{y}$ output data, $\mat{X}$ \fqEqRef{comp:ml:reg:design_matrix}, $\vec{W}$ weights}
|
||||
\desc[german]{Lineare Regression mit skalarem Bias}{Durch die Designmatrix wird der Bias in den Gewichtsvektor absorbiert}{}
|
||||
\eq{\mat{y} = \mat{X} \cdot \vec{W}}
|
||||
\end{formula}
|
||||
\begin{formula}{normal_equation}
|
||||
\desc{Normal equation}{Solves \fqEqRef{comp:ml:reg:linear:scalar_bias}}{$\mat{y}$ output data, $\mat{X}$ \fqEqRef{comp:ml:reg:linear:design_matrix}, $\vec{W}$ weights}
|
||||
\desc[german]{Normalengleichung}{Löst \fqEqRef{comp:ml:reg:linear:scalar_bias}}{}
|
||||
\eq{\vec{W} = \left(\mat{X}^\T \mat{X}\right)^{-1} \mat{X}^T \mat{y}}
|
||||
\end{formula}
|
||||
|
||||
\Subsubsection[
|
||||
\eng{Ridge regression}
|
||||
\ger{Ridge Regression}
|
||||
]{ridge}
|
||||
\TODO{ridge reg, Kernel ridge reg, gaussian process reg}
|
||||
% \Subsection[
|
||||
% \eng{Bayesian probability theory}
|
||||
% % \ger{}
|
||||
% ]{bayesian}
|
||||
|
||||
|
||||
|
||||
\Subsection[
|
||||
\eng{Gradient descent}
|
||||
\ger{Gradientenverfahren}
|
||||
]{gd}
|
||||
\TODO{TODO}
|
||||
|
||||
17
src/comp/qmb.tex
Normal file
17
src/comp/qmb.tex
Normal file
@ -0,0 +1,17 @@
|
||||
\Section[
|
||||
\eng{Quantum many-body physics}
|
||||
\ger{Quanten-Vielteilchenphysik}
|
||||
]{qmb}
|
||||
\TODO{TODO}
|
||||
\Subsection[
|
||||
\eng{Importance sampling}
|
||||
\ger{Importance sampling / Stichprobenentnahme nach Wichtigkeit}
|
||||
]{importance_sampling}
|
||||
\TODO{Monte Carlo}
|
||||
|
||||
\Subsection[
|
||||
\eng{Matrix product states}
|
||||
\ger{Matrix Produktzustände}
|
||||
]{mps}
|
||||
|
||||
|
||||
@ -1,148 +0,0 @@
|
||||
\Part[
|
||||
\eng{Computational Physics}
|
||||
\ger{Computergestützte Physik}
|
||||
]{cmp}
|
||||
\Section[
|
||||
\eng{Quantum many-body physics}
|
||||
\ger{Quanten-Vielteilchenphysik}
|
||||
]{mb}
|
||||
\TODO{TODO}
|
||||
\Subsection[
|
||||
\eng{Importance sampling}
|
||||
\ger{Importance sampling / Stichprobenentnahme nach Wichtigkeit}
|
||||
]{importance_sampling}
|
||||
\TODO{Monte Carlo}
|
||||
|
||||
\Subsection[
|
||||
\eng{Matrix product states}
|
||||
\ger{Matrix Produktzustände}
|
||||
]{mps}
|
||||
|
||||
|
||||
|
||||
\Section[
|
||||
\eng{Electronic structure theory}
|
||||
% \ger{}
|
||||
]{elsth}
|
||||
\begin{formula}{hamiltonian}
|
||||
\desc{Electronic structure Hamiltonian}{}{$\hat{T}$ kinetic energy, $\hat{V}$ electrostatic potential, $\txe$ electrons, $\txn$ nucleons}
|
||||
% \desc[german]{}{}{}
|
||||
\eq{
|
||||
\hat{H} &= \hat{T}_\txe + \hat{T}_\txn + V_{\e \leftrightarrow \e} + V_{\n \leftrightarrow \e} + V_{\n \leftrightarrow \n} \\
|
||||
\shortintertext{with}
|
||||
\hat{T}_i &= -\sum_{n=1}^{N_i} \frac{\hbar^2}{2 m_i} \vec{\nabla}^2_n \\
|
||||
\hat{V}_{i \leftrightarrow j} &= -\sum_{k,l} \frac{Z_i Z_j \e^2}{\abs{\vecr_k - \vecr_l}}
|
||||
}
|
||||
\end{formula}
|
||||
\begin{formula}{mean_field}
|
||||
\desc{Mean field approximation}{Replaces 2-particle operator by 1-particle operator}{Example for Coulumb interaction between many electrons}
|
||||
\desc[german]{Molekularfeldnäherung}{Ersetzt 2-Teilchen Operator durch 1-Teilchen Operator}{Beispiel für Coulumb Wechselwirkung zwischen Elektronen}
|
||||
\eq{
|
||||
\frac{1}{2}\sum_{i\neq j} \frac{e^2}{\abs{\vec{r}_i - \vec{r}_j}} \approx \sum_{i} V_\text{eff}(\vec{r}_i)
|
||||
}
|
||||
\end{formula}
|
||||
|
||||
|
||||
\Subsection[
|
||||
\eng{Tight-binding}
|
||||
\ger{Tight-binding}
|
||||
]{tb}
|
||||
|
||||
|
||||
\Subsection[
|
||||
\eng{Density functional theory (DFT)}
|
||||
\ger{Dichtefunktionaltheorie (DFT)}
|
||||
]{dft}
|
||||
\Subsubsection[
|
||||
\eng{Hartree-Fock}
|
||||
\ger{Hartree-Fock}
|
||||
]{hf}
|
||||
\begin{ttext}
|
||||
\eng{
|
||||
\begin{itemize}
|
||||
\item \fqEqRef{comp:misc:mean_field} theory
|
||||
\item Self-interaction free: Self interaction is cancelled out by the Fock-term
|
||||
\end{itemize}
|
||||
}
|
||||
\end{ttext}
|
||||
\begin{formula}{equation}
|
||||
\desc{Hartree-Fock equation}{}{
|
||||
$\varphi_\xi$ single particle wavefunction of $\xi$th orbital,
|
||||
$\hat{T}$ kinetic electron energy,
|
||||
$\hat{V}_{\text{en}}$ electron-nucleus attraction,
|
||||
$\hat{V}_{\text{HF}}$ \fqEqRef{comp:dft:hf:potential},
|
||||
}
|
||||
\desc[german]{Hartree-Fock Gleichung}{}{
|
||||
$\varphi_\xi$ ein-Teilchen Wellenfunktion des $\xi$-ten Orbitals,
|
||||
$\hat{T}$ kinetische Energie der Elektronen,
|
||||
$\hat{V}_{\text{en}}$ Electron-Kern Anziehung,
|
||||
$\hat{V}_{\text{HF}}$ \fqEqRef{comp:dft:hf:potential}
|
||||
}
|
||||
\eq{
|
||||
\left(\hat{T} + \hat{V}_{\text{en}} + \hat{V}_{\text{HF}}^\xi\right)\varphi_\xi(x) = \epsilon_\xi \varphi_\xi(x)
|
||||
}
|
||||
\end{formula}
|
||||
\begin{formula}{potential}
|
||||
\desc{Hartree-Fock potential}{}{}
|
||||
\desc[german]{Hartree Fock Potential}{}{}
|
||||
\eq{
|
||||
V_{\text{HF}}^\xi(\vecr) =
|
||||
\sum_{\vartheta} \int \d x'
|
||||
\frac{e^2}{\abs{\vecr - \vecr'}}
|
||||
\left(
|
||||
\underbrace{\abs{\varphi_\xi(x')}^2}_{\text{Hartree-Term}}
|
||||
- \underbrace{\frac{\varphi_{\vartheta}^*(x') \varphi_{\xi}(x') \varphi_{\vartheta}(x)}{\varphi_\xi(x)}}_{\text{Fock-Term}}
|
||||
\right)
|
||||
}
|
||||
\end{formula}
|
||||
\begin{formula}{scf}
|
||||
\desc{Self-consistend field cycle}{}{}
|
||||
% \desc[german]{}{}{}
|
||||
\ttxt{
|
||||
\eng{
|
||||
\begin{enumerate}
|
||||
\item Initial guess for $\psi$
|
||||
\item Solve SG for each particle
|
||||
\item Make new guess for $\psi$
|
||||
\end{enumerate}
|
||||
}
|
||||
}
|
||||
\end{formula}
|
||||
|
||||
\Section[
|
||||
\eng{Atomic dynamics}
|
||||
% \ger{}
|
||||
]{ad}
|
||||
\Subsection[
|
||||
\eng{Kohn-Sham}
|
||||
\ger{Kohn-Sham}
|
||||
]{ks}
|
||||
\TODO{TODO}
|
||||
|
||||
\Subsection[
|
||||
\eng{Born-Oppenheimer Approximation}
|
||||
\ger{Born-Oppenheimer Näherung}
|
||||
]{bo}
|
||||
\TODO{TODO, BO surface}
|
||||
|
||||
\Subsection[
|
||||
\eng{Molecular Dynamics}
|
||||
\ger{Molekulardynamik}
|
||||
]{md}
|
||||
\begin{ttext}
|
||||
\eng{Statistical method}
|
||||
|
||||
\end{ttext}
|
||||
|
||||
\TODO{ab-initio MD, force-field MD}
|
||||
|
||||
|
||||
|
||||
\Section[
|
||||
\eng{Gradient descent}
|
||||
\ger{Gradientenverfahren}
|
||||
]{gd}
|
||||
\TODO{TODO}
|
||||
|
||||
|
||||
|
||||
@ -44,3 +44,4 @@
|
||||
\val{\NA\,e}{}
|
||||
}
|
||||
\end{formula}
|
||||
|
||||
|
||||
@ -8,6 +8,15 @@
|
||||
\desc[german]{Elektrisches Feld}{Umgibt geladene Teilchen}{}
|
||||
\quantity{\vec{\E}}{\volt\per\m=\kg\m\per\s^3\ampere}{v}
|
||||
\end{formula}
|
||||
|
||||
\def\Epotential{\phi}
|
||||
\begin{formula}{electric_scalar_potential}
|
||||
\desc{Electric potential}{Work required to move a unit of charge between two points}{}
|
||||
\desc[german]{Elektrisches Potential}{Benötigte Arbeit um eine Einheitsladung zwischen zwei Punkten zu bewegen}{}
|
||||
\quantity{\Epotential}{\volt=\kg\m^2\per\s^3\ampere}{s}
|
||||
\eq{\Epotential = -\int \vec{\E} \cdot\d\vecr}
|
||||
\end{formula}
|
||||
|
||||
\begin{formula}{gauss_law}
|
||||
\desc{Gauss's law for electric fields}{Electric flux through a closed surface is proportional to the electric charge}{$S$ closed surface}
|
||||
\desc[german]{Gaußsches Gesetz für elektrische Felder}{Der magnetische Fluss durch eine geschlossene Fläche ist proportional zur elektrischen Ladung}{$S$ geschlossene Fläche}
|
||||
@ -15,8 +24,8 @@
|
||||
\end{formula}
|
||||
|
||||
\begin{formula}{permittivity}
|
||||
\desc{Permittivity}{Electric polarizability of a dielectric material}{}
|
||||
\desc[german]{Permitivität}{Dielektrische Konstante\\Elektrische Polarisierbarkeit eines dielektrischen Materials}{}
|
||||
\desc{Permittivity}{Dieletric function\\Electric polarizability of a dielectric material}{}
|
||||
\desc[german]{Permitivität}{Dielektrische Konstante / Dielektrische Funktion\\Elektrische Polarisierbarkeit eines dielektrischen Materials}{}
|
||||
\quantity{\epsilon}{\ampere\s\per\volt\m=\farad\per\m=\coulomb\per\volt\m=C^2\per\newton\m^2=\ampere^2\s^4\per\kg\m^3}{}
|
||||
\end{formula}
|
||||
\begin{formula}{relative_permittivity}
|
||||
@ -46,6 +55,27 @@
|
||||
\begin{formula}{dielectric_polarization_density}
|
||||
\desc{Dielectric polarization density}{}{\ConstRef{vacuum_permittivity}, \QtyRef{electric_susceptibility}, \QtyRef{electric_field}}
|
||||
\desc[german]{Dielektrische Polarisationsdichte}{}{}
|
||||
\quantity{\vec{P}}{\coulomb\per\m^2}{v}
|
||||
\eq{\vec{P} = \epsilon_0 \chi_\txe \vec{\E}}
|
||||
\end{formula}
|
||||
|
||||
\begin{formula}{electric_displacement_field}
|
||||
\desc{Electric displacement field}{}{\ConstRef{vacuum_permittivity}, \QtyRef{electric_field}, \QtyRef{dielectric_polarization_density}}
|
||||
\desc[german]{Elektrische Flussdichte / dielektrische Verschiebung}{}{}
|
||||
\quantity{\vec{D}}{\coulomb\per\m^2=\ampere\s\per\m^2}{v}
|
||||
\eq{\vec{D} = \epsilon_0 \vec{\E} + \vec{P}}
|
||||
\end{formula}
|
||||
|
||||
\begin{formula}{electric_flux}
|
||||
\desc{Electric flux}{through area $\vec{A}$}{\QtyRef{electric_displacement_field}}
|
||||
\desc[german]{Elektrischer Fluss}{durch die Fläche $\vec{A}$}{}
|
||||
\eq{\Phi_\txE = \int_A \vec{D}\cdot \d \vec{A}}
|
||||
\end{formula}
|
||||
|
||||
\begin{formula}{power}
|
||||
\desc{Electric power}{}{$U$ \qtyRef{electric_scalar_potential}, \QtyRef{current}}
|
||||
\desc[german]{Elektrische Leistung}{}{}
|
||||
\eq{P_\text{el} = U\,I}
|
||||
\end{formula}
|
||||
|
||||
|
||||
|
||||
@ -30,6 +30,21 @@
|
||||
\eq{\vec{S} = \vec{E} \times \vec{H}}
|
||||
\end{formula}
|
||||
|
||||
\begin{formula}{electric_field}
|
||||
\desc{Electric field}{}{\QtyRef{electric_field}, \QtyRef{electric_scalar_potential}, \QtyRef{magnetic_vector_potential}}
|
||||
\desc[german]{Elektrisches Feld}{}{}
|
||||
\eq{\vec{\E} = -\Grad\Epotential - \pdv{\vec{A}}{t}}
|
||||
\end{formula}
|
||||
|
||||
\begin{formula}{hamiltonian}
|
||||
\desc{Hamiltonian of a particle in an electromagnetic field}{In the \fqEqRef{ed:em:gauge:coulomb}}{\QtyRef{mass}, $\hat{p}$ \fqEqRef{qm:se:momentum_operator}, \QtyRef{charge}, \QtyRef{magnetic_vector_potential}, \ConstRef{speed_of_light}}
|
||||
\desc[german]{Hamiltonian eines Teilchens im elektromagnetischen Feld}{In der \fqEqRef{ed:em:gauge:coulomb}}{}
|
||||
\eq{
|
||||
\hat{H} = \frac{1}{2m} \left[\hat{p} \ \frac{e \vec{A}}{c}\right]^2
|
||||
}
|
||||
\end{formula}
|
||||
|
||||
|
||||
\Subsection[
|
||||
\eng{Maxwell-Equations}
|
||||
\ger{Maxwell-Gleichungen}
|
||||
@ -55,6 +70,21 @@
|
||||
\Rot \vec{H} &= \vec{j} + \odv{\vec{D}}{t}
|
||||
}
|
||||
\end{formula}
|
||||
|
||||
|
||||
\Subsubsection[
|
||||
\eng{Gauges}
|
||||
\ger{Eichungen}
|
||||
]{gauge}
|
||||
\begin{formula}{coulomb}
|
||||
\desc{Coulomb gauge}{}{\QtyRef{magnetic_vector_potential}}
|
||||
\desc[german]{Coulomb-Eichung}{}{}
|
||||
\eq{
|
||||
\Div \vec{A} = 0
|
||||
}
|
||||
\end{formula}
|
||||
|
||||
|
||||
\TODO{Polarization}
|
||||
|
||||
\Subsection[
|
||||
@ -79,4 +109,3 @@
|
||||
}
|
||||
}
|
||||
\end{formula}
|
||||
|
||||
|
||||
115
src/ed/mag.te
115
src/ed/mag.te
@ -1,115 +0,0 @@
|
||||
\Section[
|
||||
\eng{Magnetic field}
|
||||
\ger{Magnetfeld}
|
||||
]{mag}
|
||||
|
||||
\begin{formula}{magnetic_flux}
|
||||
\desc{Magnetic flux}{}{$\vec{A}$ \GT{area}}
|
||||
\desc[german]{Magnetischer Fluss}{}{}
|
||||
\quantity{\PhiB}{\weber=\volt\per\s=\kg\m^2\per\s^2\A}{scalar}
|
||||
\eq{\PhiB = \iint_A \vec{B}\cdot\d\vec{A}}
|
||||
\end{formula}
|
||||
|
||||
\begin{formula}{magnetic_flux_density}
|
||||
\desc{Magnetic flux density}{Defined by \fqEqRef{ed:mag:lorentz}}{$\vec{H}$ \qtyRef{magnetic_field_intensity}, $\vec{M}$ \qtyRef{magnetization}, \ConstRef{magnetic_vacuum_permeability}}
|
||||
\desc[german]{Magnetische Flussdichte}{Definiert über \fqEqRef{ed:mag:lorentz}}{}
|
||||
\quantity{\vec{B}}{\tesla=\volt\s\per\m^2=\newton\per\ampere\m=\kg\per\ampere\s^2}{}
|
||||
\eq{\vec{B} = \mu_0 (\vec{H}+\vec{M})}
|
||||
\end{formula}
|
||||
|
||||
\begin{formula}{magnetic_field_intensity}
|
||||
\desc{Magnetic field intensity}{}{}
|
||||
\desc[german]{Magnetische Feldstärke}{}{}
|
||||
\quantity{\vec{H}}{\ampere\per\m}{vector}
|
||||
\eq{
|
||||
\vec{H} \equiv \frac{1}{\mu_0}\vec{B} - \vec{M}
|
||||
}
|
||||
\end{formula}
|
||||
|
||||
\begin{formula}{lorentz}
|
||||
\desc{Lorentz force law}{Force on charged particle}{}
|
||||
\desc[german]{Lorentzkraft}{Kraft auf geladenes Teilchen}{}
|
||||
\eq{
|
||||
\vec{F} = q \vec{\E} + q \vec{v}\times\vec{B}
|
||||
}
|
||||
\end{formula}
|
||||
|
||||
\begin{formula}{magnetic_permeability}
|
||||
\desc{Magnetic permeability}{}{$B$ \qtyRef{magnetic_flux_density}, $H$ \qtyRef{magnetic_field_intensity}}
|
||||
\desc[german]{Magnetisch Permeabilität}{}{}
|
||||
\quantity{\mu}{\henry\per\m=\volt\s\per\ampere\m}{scalar}
|
||||
\eq{\mu=\frac{B}{H}}
|
||||
\end{formula}
|
||||
\begin{formula}{magnetic_vacuum_permeability}
|
||||
\desc{Magnetic vauum permeability}{}{}
|
||||
\desc[german]{Magnetische Vakuumpermeabilität}{}{}
|
||||
\constant{\mu_0}{exp}{
|
||||
\val{1.25663706127(20)}{\henry\per\m=\newton\per\ampere^2}
|
||||
}
|
||||
\end{formula}
|
||||
\begin{formula}{relative_permeability}
|
||||
\desc{Relative permeability}{}{}
|
||||
\desc[german]{Realtive Permeabilität}{}{}
|
||||
\eq{
|
||||
\mu_\txr = \frac{\mu}{\mu_0}
|
||||
}
|
||||
\end{formula}
|
||||
|
||||
\begin{formula}{gauss_law}
|
||||
\desc{Gauss's law for magnetism}{Magnetic flux through a closed surface is $0$ \Rightarrow there are no magnetic monopoles}{$S$ closed surface}
|
||||
\desc[german]{Gaußsches Gesetz für Magnetismus}{Der magnetische Fluss durch eine geschlossene Fläche ist $0$ \Rightarrow es gibt keine magnetischen Monopole}{$S$ geschlossene Fläche}
|
||||
\eq{\PhiB = \iint_S \vec{B}\cdot\d\vec{S} = 0}
|
||||
\end{formula}
|
||||
|
||||
\begin{formula}{magnetization}
|
||||
\desc{Magnetization}{Vector field describing the density of magnetic dipoles}{}
|
||||
\desc[german]{Magnetisierung}{Vektorfeld, welches die Dichte von magnetischen Dipolen beschreibt.}{}
|
||||
\quantity{\vec{M}}{\ampere\per\m}{vector}
|
||||
\eq{\vec{M} = \odv{\vec{m}}{V} = \chi_\txm \cdot \vec{H}}
|
||||
\end{formula}
|
||||
|
||||
\begin{formula}{magnetic_moment}
|
||||
\desc{Magnetic moment}{Strength and direction of a magnetic dipole}{}
|
||||
\desc[german]{Magnetisches Moment}{Stärke und Richtung eines magnetischen Dipols}{}
|
||||
\quantity{\vec{m}}{\ampere\m^2}{vector}
|
||||
\end{formula}
|
||||
|
||||
\begin{formula}{angular_torque}
|
||||
\desc{Torque}{}{$m$ \qtyRef{magnetic_moment}}
|
||||
\desc[german]{Drehmoment}{}{}
|
||||
\eq{\vec{\tau} = \vec{m} \times \vec{B}}
|
||||
\end{formula}
|
||||
|
||||
\begin{formula}{magnetic_susceptibility}
|
||||
\desc{Susceptibility}{}{$\mu_\txr$ \fqEqRef{ed:mag:relative_permeability}}
|
||||
\desc[german]{Suszeptibilität}{}{}
|
||||
\eq{\chi_\txm = \pdv{M}{B} = \mu_\txr - 1}
|
||||
\end{formula}
|
||||
|
||||
|
||||
|
||||
|
||||
\Subsection[
|
||||
\eng{Magnetic materials}
|
||||
\ger{Magnetische Materialien}
|
||||
]{materials}
|
||||
\begin{formula}{paramagnetism}
|
||||
\desc{Paramagnetism}{Magnetic field strengthend in the material}{$\mu$ \fqEqRef{ed:mag:magnetic_permeability}, $\chi_\txm$ \fqEqRef{ed:mag:magnetic_susceptibility}}
|
||||
\desc[german]{Paramagnetismus}{Magnetisches Feld wird im Material verstärkt}{}
|
||||
\eq{\mu_\txr &> 1 \\ \chi_\txm &> 0}
|
||||
\end{formula}
|
||||
|
||||
\begin{formula}{diamagnetism}
|
||||
\desc{Diamagnetism}{Magnetic field expelled from material}{$\mu$ \fqEqRef{ed:mag:magnetic_permeability}, $\chi_\txm$ \fqEqRef{ed:mag:magnetic_susceptibility}}
|
||||
\desc[german]{Diamagnetismus}{Magnetisches Feld wird aus dem Material gedrängt}{}
|
||||
\eq{0 < \mu_\txr < 1 \\ -1 < \chi_\txm < 0}
|
||||
\end{formula}
|
||||
|
||||
\begin{formula}{ferromagnetism}
|
||||
\desc{Ferromagnetism}{Magnetic moments align to external magnetic field and stay aligned when the field is turned off (Remanescence)}{$\mu$ \fqEqRef{ed:mag:magnetic_permeability}, $\chi_\txm$ \fqEqRef{ed:mag:magnetic_susceptibility}}
|
||||
\desc[german]{Ferromagnetismus}{Magnetische Momente werden am äußeren Feld ausgerichtet und behalten diese ausrichtung auch wenn das Feld abgeschaltet wird (Remanenz)}{}
|
||||
\eq{
|
||||
\mu_\txr \gg 1
|
||||
}
|
||||
\end{formula}
|
||||
|
||||
@ -17,6 +17,13 @@
|
||||
\eq{\vec{B} = \mu_0 (\vec{H}+\vec{M})}
|
||||
\end{formula}
|
||||
|
||||
\begin{formula}{magnetic_vector_potential}
|
||||
\desc{Magnetic vector potential}{}{}
|
||||
\desc[german]{Magnetisches Vektorpotential}{}{}
|
||||
\quantity{\vec{A}}{\tesla\m=\volt\s\per\m=\kg\m\per\s^2\ampere}{ievs}
|
||||
\eq{\Rot\vec{A}(\vecr) = \vec{B}(\vecr)}
|
||||
\end{formula}
|
||||
|
||||
\begin{formula}{magnetic_field_intensity}
|
||||
\desc{Magnetic field intensity}{}{}
|
||||
\desc[german]{Magnetische Feldstärke}{}{}
|
||||
|
||||
103
src/ed/optics.tex
Normal file
103
src/ed/optics.tex
Normal file
@ -0,0 +1,103 @@
|
||||
\Section[
|
||||
\eng{Optics}
|
||||
\ger{Optik}
|
||||
]{optics}
|
||||
\begin{ttext}
|
||||
\eng{Properties of light and its interactions with matter}
|
||||
\ger{Ausbreitung von Licht und die Interaktion mit Materie}
|
||||
\end{ttext}
|
||||
\separateEntries
|
||||
|
||||
\begin{formula}{refraction_index}
|
||||
\eng[cm]{speed of light in the medium}
|
||||
\ger[cm]{Lichtgeschwindigkeit im Medium}
|
||||
\desc{Refraction index}{}{\QtyRef{relative_permittivity}, \QtyRef{relative_permeability}, \ConstRef{speed_of_light}, $c_\txM$ \gt{cm}}
|
||||
\desc[german]{Brechungsindex}{}{}
|
||||
\quantity{\complex{n}}{}{s}
|
||||
\eq{
|
||||
\complex{n} = \nreal + i\ncomplex
|
||||
}
|
||||
\eq{
|
||||
n = \sqrt{\epsilon_\txr \mu_\txr}
|
||||
}
|
||||
\eq{
|
||||
n = \frac{c_0}{c_\txM}
|
||||
}
|
||||
\end{formula}
|
||||
|
||||
\TODO{what does the complex part of the dielectric function represent?}
|
||||
|
||||
\begin{formula}{refraction_index_real}
|
||||
\desc{Real part of the refraction index}{}{}
|
||||
\desc[german]{Reller Teil des Brechungsindex}{}{}
|
||||
\quantity{\nreal}{}{s}
|
||||
\end{formula}
|
||||
\begin{formula}{refraction_index_complex}
|
||||
\desc{Extinction coefficient}{Complex part of the refraction index}{\GT{sometimes} $\kappa$}
|
||||
\desc[german]{Auslöschungskoeffizient}{Komplexer Teil des Brechungsindex}{}
|
||||
\quantity{\ncomplex}{}{s}
|
||||
\end{formula}
|
||||
|
||||
\begin{formula}{reflectivity}
|
||||
\desc{Reflectio}{}{\QtyRef{refraction_index}}
|
||||
% \desc[german]{}{}{}
|
||||
\eq{
|
||||
R = \abs{\frac{\complex{n}-1}{\complex{n}+1}}
|
||||
}
|
||||
\end{formula}
|
||||
|
||||
\begin{formula}{snell}
|
||||
\desc{Snell's law}{}{$\nreal_i$ \qtyRef{refraction_index_real}, $\theta_i$ incidence angle (normal to the surface)}
|
||||
\desc[german]{Snelliussches Brechungsgesetz}{}{$n_i$ \qtyRef{refraction_index}, $\theta_i$ Einfallswinkel (normal zur Fläche)}
|
||||
\eq{\nreal_1 \sin\theta_1 = \nreal_2\sin\theta_2}
|
||||
\end{formula}
|
||||
|
||||
\begin{formula}{group_velocity}
|
||||
\desc{Group velocity}{Velocity with which the envelope of a wave propagates through space}{\QtyRef{angular_frequency}, \QtyRef{angular_wavenumber}}
|
||||
\desc[german]{Gruppengeschwindigkeit}{Geschwindigkeit, mit sich die Einhülende einer Welle ausbreitet}{}
|
||||
\eq{
|
||||
v_\txg \equiv \pdv{\omega}{k}
|
||||
}
|
||||
\end{formula}
|
||||
\begin{formula}{phase_velocity}
|
||||
\desc{Phase velocity}{Velocity with which a wave propagates through a medium}{\QtyRef{angular_frequency}, \QtyRef{angular_wavenumber}, \QtyRef{wavelength}, \QtyRef{time_period}}
|
||||
\desc[german]{Phasengeschwindigkeit}{Geschwindigkeit, mit der sich eine Welle im Medium ausbreitet}{}
|
||||
\eq{
|
||||
v_\txp = \frac{\omega}{k} = \frac{\lambda}{T}
|
||||
}
|
||||
\end{formula}
|
||||
|
||||
\begin{formula}{absorption_coefficient}
|
||||
\desc{Absorption coefficient}{Intensity reduction while traversing a medium, not necessarily by energy transfer to the medium}{\QtyRef{refraction_index_complex}, \ConstRef{speed_of_light}, \QtyRef{angular_frequency}}
|
||||
\desc[german]{Absoprtionskoeffizient}{Intensitätsverringerung beim Druchgang eines Mediums, nicht zwingend durch Energieabgabe an Medium}{}
|
||||
\quantity{\alpha}{\per\cm}{s}
|
||||
\eq{
|
||||
\alpha &= 2\ncomplex \frac{\omega}{c} \\
|
||||
\alpha &= \frac{\omega}{nc} \epsilon^\prime \text{\TODO{For direct band gaps; from adv. sc: sheet 10 2b). Check which is correct}}
|
||||
}
|
||||
\end{formula}
|
||||
|
||||
|
||||
\begin{formula}{intensity}
|
||||
\desc{Electromagnetic radiation intensity}{Surface power density}{$S$ \fqEqRef{ed:poynting}}
|
||||
\desc[german]{Elektromagnetische Strahlungsintensität}{Flächenleistungsdichte}{}
|
||||
\quantity{I}{\watt\per\m^2=\k\per\s^3}{s}
|
||||
\eq{I = \abs{\braket{S}_t}}
|
||||
\end{formula}
|
||||
|
||||
% \begin{formula}{lambert_beer_law}
|
||||
% \desc{Beer-Lambert law}{Intensity in an absorbing medium}{$E_\lambda$ extinction, \QtyRef{absorption_coefficient}, \QtyRef{concentration}, $d$ Thickness of the medium}
|
||||
% \desc[german]{Lambert-beersches Gesetz}{Intensität in einem absorbierenden Medium}{$E_\lambda$ Extinktion, \QtyRef{refraction_index_complex}, \QtyRef{concentration}, $d$ Dicke des Mediums}
|
||||
% \eq{
|
||||
% E_\lambda = \log_{10} \frac{I_0}{I} = \kappa c d \\
|
||||
% }
|
||||
% \end{formula}
|
||||
\begin{formula}{lambert_beer_law}
|
||||
\desc{Beer-Lambert law}{Intensity in an absorbing medium}{\QtyRef{intensity}, \QtyRef{absorption_coefficient}, $z$ penetration depth}
|
||||
\desc[german]{Lambert-beersches Gesetz}{Intensität in einem absorbierenden Medium}{\QtyRef{intensity}, \QtyRef{absorption_coefficient}, $z$ Eindringtiefe}
|
||||
\eq{
|
||||
I(z) = I_0 \e^{-\kappa z}
|
||||
}
|
||||
\end{formula}
|
||||
|
||||
|
||||
54
src/img/cm/sc_junction_metal_n_sc.tex
Normal file
54
src/img/cm/sc_junction_metal_n_sc.tex
Normal file
@ -0,0 +1,54 @@
|
||||
\begin{tikzpicture}[scale=0.9]
|
||||
|
||||
\pgfmathsetmacro{\tkW}{8} % Total width
|
||||
\pgfmathsetmacro{\tkH}{5} % Total height
|
||||
% left
|
||||
\pgfmathsetmacro{\tkLx}{0} % Start
|
||||
\pgfmathsetmacro{\tkLW}{2} % Right width
|
||||
\pgfmathsetmacro{\tkLyshift}{0.0} % y-shift
|
||||
\pgfmathsetmacro{\tkLBendH}{0} % Band bending height
|
||||
\pgfmathsetmacro{\tkLBendW}{0} % Band bending width
|
||||
\pgfmathsetmacro{\tkLEV}{4.0+\tkLyshift}% Vacuum energy
|
||||
\pgfmathsetmacro{\tkLEf}{1.5+\tkLyshift}% Fermi level energy
|
||||
% right
|
||||
\pgfmathsetmacro{\tkRx}{\tkLW} % Left start
|
||||
\pgfmathsetmacro{\tkRW}{\tkW-\tkRx} % Left width
|
||||
\pgfmathsetmacro{\tkRyshift}{-0.5} % y-shift
|
||||
\pgfmathsetmacro{\tkRBendH}{0.5} % Band bending height
|
||||
\pgfmathsetmacro{\tkRBendW}{\tkRW/4} % Band bending width
|
||||
\pgfmathsetmacro{\tkREv}{0.7+\tkRyshift}% Valence band energy
|
||||
\pgfmathsetmacro{\tkREc}{2.4+\tkRyshift}% Conduction band energy
|
||||
\pgfmathsetmacro{\tkREV}{4.0+\tkRyshift}% Vacuum energy
|
||||
\pgfmathsetmacro{\tkREf}{2.0+\tkRyshift}% Fermi level energy
|
||||
|
||||
% materials
|
||||
\draw[sc metal] (0,0) rectangle (\tkLW,\tkH);
|
||||
\node at (\tkLW/2,\tkH-0.2) {\GT{metal}};
|
||||
\path[sc n type] (\tkRx,0) rectangle (\tkW,\tkH);
|
||||
\node at (\tkRx+\tkRW/2,\tkH-0.2) {\GT{n-type}};
|
||||
\path[sc separate] (\tkLW,0) -- (\tkLW,\tkH);
|
||||
|
||||
% axes
|
||||
\draw[->] (0,0) -- (\tkW+0.2,0) node[anchor=north] {$x$};
|
||||
\draw[->] (0,0) -- (0,\tkH+0.2) node[anchor=east] {$E$};
|
||||
|
||||
% right bands
|
||||
\path[sc occupied] (\tkRx, 0) -- \rightBandUp{}{\tkREv} -- (\tkW, 0) -- cycle;
|
||||
\draw[sc band con] \rightBandUp{$\Econd$}{\tkREc};
|
||||
\draw[sc band val] \rightBandUp{$\Evalence$}{\tkREv};
|
||||
\draw[sc band vac] (0,\tkLEV) -- \rightBandUp{$\Evac$}{\tkREV};
|
||||
\draw[sc fermi level] \rightBand{$\Efermi$}{\tkREf};
|
||||
% left bands
|
||||
\path[sc occupied] (0,0) rectangle (\tkLW,\tkLEf);
|
||||
\draw[sc fermi level] \leftBand{$\Efermi$}{\tkLEf};
|
||||
|
||||
% work functions
|
||||
\drawDArrow{\tkLW/2}{\tkLEf}{\tkLEV}{$e\Phi_\txM$}
|
||||
\drawDArrow{\tkRx+\tkRW*3/4}{\tkREf}{\tkREV}{$e\Phi_\txS$}
|
||||
\drawDArrow{\tkRx+\tkRW*2/4}{\tkREc}{\tkREV}{$e\chi$}
|
||||
% barrier height
|
||||
\drawDArrow{\tkRx+\tkRBendW}{\tkREc}{\tkREc+\tkRBendH}{$eU_\text{Bias}$}
|
||||
\drawDArrow{\tkRx}{\tkREf}{\tkREc+\tkRBendH}{$e\Phi_\txB$}
|
||||
|
||||
\end{tikzpicture}
|
||||
|
||||
49
src/img/cm/sc_junction_metal_n_sc_separate.tex
Normal file
49
src/img/cm/sc_junction_metal_n_sc_separate.tex
Normal file
@ -0,0 +1,49 @@
|
||||
\begin{tikzpicture}[scale=0.9]
|
||||
|
||||
\pgfmathsetmacro{\tkW}{8} % Total width
|
||||
\pgfmathsetmacro{\tkH}{5} % Total height
|
||||
% left
|
||||
\pgfmathsetmacro{\tkLx}{0} % Start
|
||||
\pgfmathsetmacro{\tkLW}{2} % Right width
|
||||
\pgfmathsetmacro{\tkLyshift}{0.0} % y-shift
|
||||
\pgfmathsetmacro{\tkLBendH}{0} % Band bending height
|
||||
\pgfmathsetmacro{\tkLBendW}{0} % Band bending width
|
||||
\pgfmathsetmacro{\tkLEV}{4.0+\tkLyshift}% Vacuum energy
|
||||
\pgfmathsetmacro{\tkLEf}{1.5+\tkLyshift}% Fermi level energy
|
||||
% right
|
||||
\pgfmathsetmacro{\tkRx}{4} % Left start
|
||||
\pgfmathsetmacro{\tkRW}{\tkW-\tkRx} % Left width
|
||||
\pgfmathsetmacro{\tkRyshift}{0} % y-shift
|
||||
\pgfmathsetmacro{\tkRBendH}{0.5} % Band bending height
|
||||
\pgfmathsetmacro{\tkRBendW}{\tkRW/4} % Band bending width
|
||||
\pgfmathsetmacro{\tkREv}{0.7+\tkRyshift}% Valence band energy
|
||||
\pgfmathsetmacro{\tkREc}{2.4+\tkRyshift}% Conduction band energy
|
||||
\pgfmathsetmacro{\tkREV}{4.0+\tkRyshift}% Vacuum energy
|
||||
\pgfmathsetmacro{\tkREf}{2.0+\tkRyshift}% Fermi level energy
|
||||
|
||||
% materials
|
||||
\draw[sc metal] (0,0) rectangle (\tkLW,\tkH);
|
||||
\node at (\tkLW/2,\tkH-0.2) {\GT{metal}};
|
||||
\path[sc n type] (\tkRx,0) rectangle (\tkW,\tkH);
|
||||
\node at (\tkRx+\tkRW/2,\tkH-0.2) {\GT{n-type}};
|
||||
|
||||
% axes
|
||||
\draw[->] (0,0) -- (\tkW+0.2,0) node[anchor=north] {$x$};
|
||||
\draw[->] (0,0) -- (0,\tkH+0.2) node[anchor=east] {$E$};
|
||||
|
||||
% right bands
|
||||
\path[sc occupied] (\tkRx, 0) -- \rightBand{}{\tkREv} -- (\tkW, 0) -- cycle;
|
||||
\draw[sc band con] \rightBand{$\Econd$}{\tkREc};
|
||||
\draw[sc band val] \rightBand{$\Evalence$}{\tkREv};
|
||||
\draw[sc band vac] (0,\tkLEV) -- \rightBand{$\Evac$}{\tkREV};
|
||||
\draw[sc fermi level] \rightBand{$\Efermi$}{\tkREf};
|
||||
% left bands
|
||||
\path[sc occupied] (0,0) rectangle (\tkLW,\tkLEf);
|
||||
\draw[sc fermi level] \leftBand{$\Efermi$}{\tkLEf};
|
||||
|
||||
% work functions
|
||||
\drawDArrow{\tkLW/2}{\tkLEf}{\tkLEV}{$e\Phi_\txM$}
|
||||
\drawDArrow{\tkRx+\tkRW*2/3}{\tkREf}{\tkREV}{$e\Phi_\txS$}
|
||||
\drawDArrow{\tkRx+\tkRW*1/3}{\tkREc}{\tkREV}{$e\chi$}
|
||||
|
||||
\end{tikzpicture}
|
||||
51
src/img/cm/sc_junction_ohmic.tex
Normal file
51
src/img/cm/sc_junction_ohmic.tex
Normal file
@ -0,0 +1,51 @@
|
||||
\begin{tikzpicture}[scale=1]
|
||||
|
||||
\pgfmathsetmacro{\tkW}{8} % Total width
|
||||
\pgfmathsetmacro{\tkH}{5} % Total height
|
||||
% left
|
||||
\pgfmathsetmacro{\tkLx}{0} % Start
|
||||
\pgfmathsetmacro{\tkLW}{2} % Right width
|
||||
\pgfmathsetmacro{\tkLyshift}{-0.5} % y-shift
|
||||
\pgfmathsetmacro{\tkLBendH}{0} % Band bending height
|
||||
\pgfmathsetmacro{\tkLBendW}{0} % Band bending width
|
||||
\pgfmathsetmacro{\tkLEV}{4.0+\tkLyshift}% Vacuum energy
|
||||
\pgfmathsetmacro{\tkLEf}{2.5+\tkLyshift}% Fermi level energy
|
||||
% right
|
||||
\pgfmathsetmacro{\tkRx}{\tkLW} % Left start
|
||||
\pgfmathsetmacro{\tkRW}{\tkW-\tkRx} % Left width
|
||||
\pgfmathsetmacro{\tkRyshift}{0} % y-shift
|
||||
\pgfmathsetmacro{\tkRBendH}{-0.5} % Band bending height
|
||||
\pgfmathsetmacro{\tkRBendW}{\tkRW/4} % Band bending width
|
||||
\pgfmathsetmacro{\tkREv}{0.7+\tkRyshift}% Valence band energy
|
||||
\pgfmathsetmacro{\tkREc}{2.5+\tkRyshift}% Conduction band energy
|
||||
\pgfmathsetmacro{\tkREV}{4.0+\tkRyshift}% Vacuum energy
|
||||
\pgfmathsetmacro{\tkREf}{2.0+\tkRyshift}% Fermi level energy
|
||||
|
||||
% materials
|
||||
\draw[sc metal] (0,0) rectangle (\tkLW,\tkH);
|
||||
\node at (\tkLW/2,\tkH-0.2) {\GT{metal}};
|
||||
\path[sc n type] (\tkRx,0) rectangle (\tkW,\tkH);
|
||||
\node at (\tkRx+\tkRW/2,\tkH-0.2) {\GT{n-type}};
|
||||
\path[sc separate] (\tkRx,0) -- (\tkRx,\tkH);
|
||||
|
||||
\drawAxes
|
||||
|
||||
% right bands
|
||||
\path[sc occupied] (\tkRx, 0) -- \rightBandAuto{}{\tkREv} -- (\tkW, 0) -- cycle;
|
||||
\draw[sc band con] \rightBandAuto{$\Econd$}{\tkREc};
|
||||
\draw[sc band val] \rightBandAuto{$\Evalence$}{\tkREv};
|
||||
\draw[sc band vac] (0,\tkLEV) -- \rightBandAuto{$\Evac$}{\tkREV};
|
||||
\draw[sc fermi level] \rightBand{$\Efermi$}{\tkREf};
|
||||
% left bands
|
||||
\path[sc occupied] (0,0) rectangle (\tkLW,\tkLEf);
|
||||
\draw[sc fermi level] \leftBand{$\Efermi$}{\tkLEf};
|
||||
|
||||
% work functions
|
||||
\drawDArrow{\tkLW/2}{\tkLEf}{\tkLEV}{$e\Phi_\txM$}
|
||||
\drawDArrow{\tkRx+\tkRW*3/4}{\tkREf}{\tkREV}{$e\Phi_\txS$}
|
||||
\drawDArrow{\tkRx+\tkRW*2/4}{\tkREc}{\tkREV}{$e\chi$}
|
||||
% barrier height
|
||||
\drawDArrow{\tkRx+\tkRBendW}{\tkREc}{\tkREc-\tkRBendH}{$eU_\text{Bias}$}
|
||||
|
||||
\end{tikzpicture}
|
||||
|
||||
48
src/img/cm/sc_junction_ohmic_separate.tex
Normal file
48
src/img/cm/sc_junction_ohmic_separate.tex
Normal file
@ -0,0 +1,48 @@
|
||||
\begin{tikzpicture}[scale=1]
|
||||
|
||||
\pgfmathsetmacro{\tkW}{8} % Total width
|
||||
\pgfmathsetmacro{\tkH}{5} % Total height
|
||||
% left
|
||||
\pgfmathsetmacro{\tkLx}{0} % Start
|
||||
\pgfmathsetmacro{\tkLW}{2} % Right width
|
||||
\pgfmathsetmacro{\tkLyshift}{0.0} % y-shift
|
||||
\pgfmathsetmacro{\tkLBendH}{0} % Band bending height
|
||||
\pgfmathsetmacro{\tkLBendW}{0} % Band bending width
|
||||
\pgfmathsetmacro{\tkLEV}{4.0+\tkLyshift}% Vacuum energy
|
||||
\pgfmathsetmacro{\tkLEf}{2.5+\tkLyshift}% Fermi level energy
|
||||
% right
|
||||
\pgfmathsetmacro{\tkRx}{4} % Left start
|
||||
\pgfmathsetmacro{\tkRW}{\tkW-\tkRx} % Left width
|
||||
\pgfmathsetmacro{\tkRyshift}{0} % y-shift
|
||||
\pgfmathsetmacro{\tkRBendH}{0.5} % Band bending height
|
||||
\pgfmathsetmacro{\tkRBendW}{\tkRW/4} % Band bending width
|
||||
\pgfmathsetmacro{\tkREv}{0.7+\tkRyshift}% Valence band energy
|
||||
\pgfmathsetmacro{\tkREc}{2.5+\tkRyshift}% Conduction band energy
|
||||
\pgfmathsetmacro{\tkREV}{4.0+\tkRyshift}% Vacuum energy
|
||||
\pgfmathsetmacro{\tkREf}{2.0+\tkRyshift}% Fermi level energy
|
||||
|
||||
% materials
|
||||
\draw[sc metal] (0,0) rectangle (\tkLW,\tkH);
|
||||
\node at (\tkLW/2,\tkH-0.2) {\GT{metal}};
|
||||
\path[sc n type] (\tkRx,0) rectangle (\tkW,\tkH);
|
||||
\node at (\tkRx+\tkRW/2,\tkH-0.2) {\GT{n-type}};
|
||||
|
||||
\drawAxes
|
||||
|
||||
% right bands
|
||||
\path[sc occupied] (\tkRx, 0) -- \rightBand{}{\tkREv} -- (\tkW, 0) -- cycle;
|
||||
\draw[sc band con] \rightBand{$\Econd$}{\tkREc};
|
||||
\draw[sc band val] \rightBand{$\Evalence$}{\tkREv};
|
||||
\draw[sc band vac] (0,\tkLEV) -- \rightBand{$\Evac$}{\tkREV};
|
||||
\draw[sc fermi level] \rightBand{$\Efermi$}{\tkREf};
|
||||
% left bands
|
||||
\path[sc occupied] (0,0) rectangle (\tkLW,\tkLEf);
|
||||
\draw[sc fermi level] \leftBand{$\Efermi$}{\tkLEf};
|
||||
|
||||
% work functions
|
||||
\drawDArrow{\tkLW/2}{\tkLEf}{\tkLEV}{$e\Phi_\txM$}
|
||||
\drawDArrow{\tkRx+\tkRW*2/3}{\tkREf}{\tkREV}{$e\Phi_\txS$}
|
||||
\drawDArrow{\tkRx+\tkRW*1/3}{\tkREc}{\tkREV}{$e\chi$}
|
||||
|
||||
\end{tikzpicture}
|
||||
|
||||
65
src/img/cm/sc_junction_pn.tex
Normal file
65
src/img/cm/sc_junction_pn.tex
Normal file
@ -0,0 +1,65 @@
|
||||
\newcommand\tikzPnJunction[7]{
|
||||
\begin{tikzpicture}[scale=1.0]
|
||||
|
||||
\pgfmathsetmacro{\tkW}{8} % Total width
|
||||
\pgfmathsetmacro{\tkH}{5} % Total height
|
||||
% left
|
||||
\pgfmathsetmacro{\tkLx}{0} % Start
|
||||
\pgfmathsetmacro{\tkLW}{\tkW*#1} % Width
|
||||
\pgfmathsetmacro{\tkLyshift}{#2} % y-shift
|
||||
\pgfmathsetmacro{\tkLBendH}{#3} % Band bending height
|
||||
\pgfmathsetmacro{\tkLBendW}{\tkLW/4} % Band bending width
|
||||
\pgfmathsetmacro{\tkLEv}{0.7+\tkLyshift}% Valence band energy
|
||||
\pgfmathsetmacro{\tkLEc}{2.3+\tkLyshift}% Conduction band energy
|
||||
\pgfmathsetmacro{\tkLEV}{4.0+\tkLyshift}% Vacuum energy
|
||||
\pgfmathsetmacro{\tkLEf}{1.1+\tkLyshift}% Fermi level energy
|
||||
% right
|
||||
\pgfmathsetmacro{\tkRx}{\tkW*(1-#4)} % Start
|
||||
\pgfmathsetmacro{\tkRW}{\tkW*#4} % Width
|
||||
\pgfmathsetmacro{\tkRyshift}{#5} % y-shift
|
||||
\pgfmathsetmacro{\tkRBendH}{#6} % Band bending height
|
||||
\pgfmathsetmacro{\tkRBendW}{\tkRW/4} % Band bending width
|
||||
\pgfmathsetmacro{\tkREv}{0.7+\tkRyshift}% Valence band energy
|
||||
\pgfmathsetmacro{\tkREc}{2.3+\tkRyshift}% Conduction band energy
|
||||
\pgfmathsetmacro{\tkREV}{4.0+\tkRyshift}% Vacuum energy
|
||||
\pgfmathsetmacro{\tkREf}{1.9+\tkRyshift}% Fermi level energy
|
||||
|
||||
% materials
|
||||
\draw[sc p type] (0,0) rectangle (\tkLW,\tkH);
|
||||
\node at (\tkLW/2,\tkH-0.2) {\GT{p-type}};
|
||||
\path[sc separate] (\tkRx,0) -- (\tkRx,\tkH);
|
||||
\path[sc n type] (\tkRx,0) rectangle (\tkW,\tkH);
|
||||
\node at (\tkRx+\tkRW/2,\tkH-0.2) {\GT{n-type}};
|
||||
\path[sc separate] (\tkLW,0) -- (\tkLW,\tkH);
|
||||
|
||||
\drawAxes
|
||||
|
||||
% right bands
|
||||
\path[sc occupied] (\tkRx, 0) -- \rightBandAuto{}{\tkREv} -- (\tkW, 0) -- cycle;
|
||||
\draw[sc band con] \rightBandAuto{$\Econd$}{\tkREc};
|
||||
\draw[sc band val] \rightBandAuto{$\Evalence$}{\tkREv};
|
||||
\draw[sc band vac] \rightBandAuto{$\Evac$}{\tkREV};
|
||||
\draw[sc fermi level] \rightBand{$\Efermi$}{\tkREf};
|
||||
% left bands
|
||||
\path[sc occupied] (\tkLx, 0) -- \leftBandAuto{}{\tkLEv} -- (\tkLW, 0) -- cycle;
|
||||
\draw[sc band con] \leftBandAuto{$\Econd$}{\tkLEc};
|
||||
\draw[sc band val] \leftBandAuto{$\Evalence$}{\tkLEv};
|
||||
\draw[sc band vac] \leftBandAuto{$\Evac$}{\tkLEV};
|
||||
\draw[sc fermi level] \leftBand{$\Efermi$}{\tkLEf};
|
||||
|
||||
% work functions
|
||||
|
||||
\drawDArrow{\tkRx+\tkRW*2/3}{\tkREf}{\tkREV}{$e\Phi_\txn$}
|
||||
\drawDArrow{\tkRx+\tkRW*1/3}{\tkREc}{\tkREV}{$e\chi_\txn$}
|
||||
\drawDArrow{\tkLx+\tkLW*2/3}{\tkLEf}{\tkLEV}{$e\Phi_\txp$}
|
||||
\drawDArrow{\tkLx+\tkLW*1/3}{\tkLEc}{\tkLEV}{$e\chi_\txp$}
|
||||
% barrier height
|
||||
% \drawDArrow{\tkRx+\tkRBendW}{\tkREc}{\tkREc+\tkRBendH}{$eU_\text{Bias}$}
|
||||
% \drawDArrow{\tkRx}{\tkREf}{\tkREc+\tkRBendH}{$e\Phi_\txB$}
|
||||
#7
|
||||
|
||||
\end{tikzpicture}
|
||||
}
|
||||
% \tikzPnJunction{1/3}{0}{0}{1/3}{0}{0}{}
|
||||
% \tikzPnJunction{1/2}{0.4}{-0.4}{1/2}{-0.4}{0.4}{}
|
||||
|
||||
68
src/main.tex
68
src/main.tex
@ -22,6 +22,11 @@
|
||||
\usepackage{subcaption} % subfigures
|
||||
\usepackage[hidelinks]{hyperref} % hyperrefs for \fqEqRef, \qtyRef, etc
|
||||
\usepackage[shortlabels]{enumitem} % easily change enum symbols to i), a. etc
|
||||
\setlist{noitemsep} % no vertical space between items
|
||||
\setlist[1]{labelindent=\parindent} % < Usually a good idea
|
||||
\setlist[itemize]{leftmargin=*}
|
||||
\setlist[enumerate]{labelsep=*, leftmargin=1.5pc} % horizontal indent of items
|
||||
|
||||
\usepackage{titlesec} % colored titles
|
||||
\usepackage{array} % more array options
|
||||
\newcolumntype{C}{>{$}c<{$}} % math-mode version of "c" column type
|
||||
@ -30,10 +35,14 @@
|
||||
\usepackage{translations}
|
||||
\input{util/translation.tex}
|
||||
\input{util/colorscheme.tex}
|
||||
\input{util/colors.tex} % after colorscheme
|
||||
% GRAPHICS
|
||||
\usepackage{tikz} % drawings
|
||||
\usetikzlibrary{decorations.pathmorphing}
|
||||
\usetikzlibrary{decorations.pathreplacing} % braces
|
||||
\usetikzlibrary{calc}
|
||||
\usetikzlibrary{patterns}
|
||||
\input{util/tikz_macros}
|
||||
% speed up compilation by externalizing figures
|
||||
% \usetikzlibrary{external}
|
||||
% \tikzexternalize[prefix=tikz_figures]
|
||||
@ -78,9 +87,11 @@
|
||||
|
||||
|
||||
|
||||
\newcommand{\TODO}[1]{{\color{bright_red}TODO:#1}}
|
||||
\newcommand{\TODO}[1]{{\color{fg-red}TODO:#1}}
|
||||
\newcommand{\ts}{\textsuperscript}
|
||||
|
||||
\newcommand\printFqName{\expandafter\detokenize\expandafter{\fqname}}
|
||||
|
||||
% "automate" sectioning
|
||||
% start <section>, get heading from translation, set label
|
||||
% fqname is the fully qualified name: the keys of all previous sections joined with a ':'
|
||||
@ -145,11 +156,13 @@
|
||||
% 1: key/fully qualified name (without qty/eq/sec/const/el... prefix)
|
||||
% Equations/Formulas
|
||||
% <name>
|
||||
% \newrobustcmd{\fqEqRef}[1]{%
|
||||
\newrobustcmd{\fqEqRef}[1]{%
|
||||
% \edef\fqeqrefname{\GT{#1}}
|
||||
% \hyperref[eq:#1]{\fqeqrefname}
|
||||
\hyperref[f:#1]{\GT{#1}}%
|
||||
}
|
||||
|
||||
% Section
|
||||
% <name>
|
||||
\newrobustcmd{\fqSecRef}[1]{%
|
||||
@ -178,7 +191,7 @@
|
||||
% Element from periodic table
|
||||
% <symbol>
|
||||
\newrobustcmd{\elRef}[1]{%
|
||||
\hyperref[el:#1]{{\color{dark0_hard}#1}}%
|
||||
\hyperref[el:#1]{{\color{fg0}#1}}%
|
||||
}
|
||||
% <name>
|
||||
\newrobustcmd{\ElRef}[1]{%
|
||||
@ -197,12 +210,12 @@
|
||||
% Write directlua command to aux and run it as well
|
||||
% This one expands the argument in the aux file:
|
||||
\newcommand\directLuaAuxExpand[1]{
|
||||
\immediate\write\luaauxfile{\noexpand\directlua{#1}}
|
||||
\immediate\write\luaAuxFile{\noexpand\directlua{#1}}
|
||||
\directlua{#1}
|
||||
}
|
||||
% This one does not:
|
||||
\newcommand\directLuaAux[1]{
|
||||
\immediate\write\luaauxfile{\noexpand\directlua{\detokenize{#1}}}
|
||||
\immediate\write\luaAuxFile{\noexpand\directlua{\detokenize{#1}}}
|
||||
\directlua{#1}
|
||||
}
|
||||
% read
|
||||
@ -212,11 +225,20 @@
|
||||
% \@latex@warning@no@line{"Lua aux not loaded!"}
|
||||
}
|
||||
\def\luaAuxLoaded{False}
|
||||
|
||||
% write
|
||||
\newwrite\luaauxfile
|
||||
\immediate\openout\luaauxfile=\jobname.lua.aux
|
||||
\immediate\write\luaauxfile{\noexpand\def\noexpand\luaAuxLoaded{True}}%
|
||||
\AtEndDocument{\immediate\closeout\luaauxfile}
|
||||
\newwrite\luaAuxFile
|
||||
\immediate\openout\luaAuxFile=\jobname.lua.aux
|
||||
\immediate\write\luaAuxFile{\noexpand\def\noexpand\luaAuxLoaded{True}}%
|
||||
\AtEndDocument{\immediate\closeout\luaAuxFile}
|
||||
|
||||
% Create a text file with relevant labels for vim-completion
|
||||
\newwrite\labelsFile
|
||||
\immediate\openout\labelsFile=\jobname.labels.txt
|
||||
\newcommand\storeLabel[1]{
|
||||
\immediate\write\labelsFile{#1}%
|
||||
}
|
||||
\AtEndDocument{\immediate\closeout\labelsFile}
|
||||
|
||||
\input{circuit.tex}
|
||||
\input{util/macros.tex}
|
||||
@ -262,7 +284,7 @@
|
||||
|
||||
\input{util/translations.tex}
|
||||
|
||||
% \InputOnly{math}
|
||||
% \InputOnly{ch}
|
||||
|
||||
\Input{math/math}
|
||||
\Input{math/linalg}
|
||||
@ -277,10 +299,11 @@
|
||||
\Input{ed/el}
|
||||
\Input{ed/mag}
|
||||
\Input{ed/em}
|
||||
\Input{ed/optics}
|
||||
\Input{ed/misc}
|
||||
|
||||
\Input{quantum_mechanics}
|
||||
\Input{atom}
|
||||
\Input{qm/qm}
|
||||
\Input{qm/atom}
|
||||
|
||||
\Input{cm/cm}
|
||||
\Input{cm/crystal}
|
||||
@ -290,29 +313,30 @@
|
||||
\Input{cm/semiconductors}
|
||||
\Input{cm/misc}
|
||||
\Input{cm/techniques}
|
||||
\Input{cm/topo}
|
||||
|
||||
\Input{topo}
|
||||
|
||||
\Input{particle}
|
||||
|
||||
\Input{quantum_computing}
|
||||
|
||||
\Input{computational}
|
||||
|
||||
\Input{quantities}
|
||||
\Input{constants}
|
||||
\Input{comp/comp}
|
||||
\Input{comp/qmb}
|
||||
\Input{comp/elsth}
|
||||
\Input{comp/ad}
|
||||
\Input{comp/ml}
|
||||
|
||||
\Input{ch/periodic_table} % only definitions
|
||||
\Input{ch/ch}
|
||||
|
||||
|
||||
% \newpage
|
||||
% \Input{test}
|
||||
|
||||
\newpage
|
||||
\Part[
|
||||
\eng{Appendix}
|
||||
\ger{Anhang}
|
||||
]{appendix}
|
||||
% \listofmyenv
|
||||
\Input{quantities}
|
||||
\Input{constants}
|
||||
|
||||
% \listofquantities
|
||||
\listoffigures
|
||||
\listoftables
|
||||
@ -321,6 +345,8 @@
|
||||
\ger{Liste der Elemente}
|
||||
]{elements}
|
||||
\printAllElements
|
||||
\newpage
|
||||
\Input{test}
|
||||
|
||||
% \bibliographystyle{plain}
|
||||
% \bibliography{ref}
|
||||
|
||||
@ -145,7 +145,7 @@
|
||||
\begin{formula}{delta_of_function}
|
||||
\desc{Dirac-Delta of a function}{}{$g(x_0) = 0$}
|
||||
\desc[german]{Dirac-Delta einer Funktion}{}{}
|
||||
\eq{\delta(f(x)) = \frac{\delta(x-x_0)}{\abs{g'(x_0)}}}
|
||||
\eq{\delta(f(x)) = \frac{\delta(x-x_0)}{\abs{g^\prime(x_0)}}}
|
||||
\end{formula}
|
||||
|
||||
\begin{formula}{geometric_series}
|
||||
@ -179,6 +179,36 @@
|
||||
}
|
||||
\end{formula}
|
||||
|
||||
\Subsection[
|
||||
\eng{Vector calculus}
|
||||
\ger{Vektor Analysis}
|
||||
]{vec}
|
||||
\begin{formula}{laplace}
|
||||
\desc{Laplace operator}{}{}
|
||||
\desc[german]{Laplace-Operator}{}{}
|
||||
\eq{\laplace = \Grad^2 = \pdv[2]{}{x} + \pdv[2]{}{y} + \pdv[2]{}{z}}
|
||||
\end{formula}
|
||||
\Subsubsection[
|
||||
\eng{Spherical symmetry}
|
||||
\ger{Kugelsymmetrie}
|
||||
]{sphere}
|
||||
\begin{formula}{coordinates}
|
||||
\desc{Spherical coordinates}{}{}
|
||||
\desc[german]{Kugelkoordinaten}{}{}
|
||||
\eq{
|
||||
x &= r \sin\phi,\cos\theta \\
|
||||
y &= r \cos\phi,\cos\theta \\
|
||||
z &= r \sin\theta
|
||||
}
|
||||
\end{formula}
|
||||
|
||||
\begin{formula}{laplace}
|
||||
\desc{Laplace operator}{}{}
|
||||
\desc[german]{Laplace-Operator}{}{}
|
||||
\eq{\Grad^2 = \laplace = \frac{1}{r^2} \pdv{}{r} \left(r^2 \pdv{}{r}\right)}
|
||||
\end{formula}
|
||||
|
||||
|
||||
\Subsection[
|
||||
\eng{Integrals}
|
||||
\ger{Integralrechnung}
|
||||
@ -187,7 +217,7 @@
|
||||
\desc{Partial integration}{}{}
|
||||
\desc[german]{Partielle integration}{}{}
|
||||
\eq{
|
||||
\int_a^b f'(x)\cdot g(x) \d x= \left[f(x)\cdot g(x)\right]_a^b - \int_a^b f(x)\cdot g'(x) \d x
|
||||
\int_a^b f^\prime(x)\cdot g(x) \d x= \left[f(x)\cdot g(x)\right]_a^b - \int_a^b f(x)\cdot g^\prime(x) \d x
|
||||
}
|
||||
\end{formula}
|
||||
|
||||
@ -195,7 +225,7 @@
|
||||
\desc{Integration by substitution}{}{}
|
||||
\desc[german]{Integration durch Substitution}{}{}
|
||||
\eq{
|
||||
\int_a^b f(g(x))\,g'(x) \d x = \int_{g(a)}^{g(b)} f(z) \d z
|
||||
\int_a^b f(g(x))\,g^\prime(x) \d x = \int_{g(a)}^{g(b)} f(z) \d z
|
||||
}
|
||||
\end{formula}
|
||||
|
||||
@ -203,7 +233,7 @@
|
||||
\desc{Gauss's theorem / Divergence theorem}{Divergence in a volume equals the flux through the surface}{$A = \partial V$}
|
||||
\desc[german]{Satz von Gauss}{Divergenz in einem Volumen ist gleich dem Fluss durch die Oberfläche}{}
|
||||
\eq{
|
||||
\iiint_V (\Div{\vec{F}}) \d V = \oiint_A \vec{F} \cdot \d\vec{A}
|
||||
\iiint_V \Div{\vec{F}} \d V = \oiint_A \vec{F} \cdot \d\vec{A}
|
||||
}
|
||||
\end{formula}
|
||||
|
||||
@ -239,15 +269,6 @@
|
||||
}
|
||||
\end{formula}
|
||||
|
||||
\begin{formula}{spherical-coordinates}
|
||||
\desc{Spherical coordinates}{}{}
|
||||
\desc[german]{Kugelkoordinaten}{}{}
|
||||
\eq{
|
||||
x &= r \sin\phi,\cos\theta \\
|
||||
y &= r \cos\phi,\cos\theta \\
|
||||
z &= r \sin\theta
|
||||
}
|
||||
\end{formula}
|
||||
\begin{formula}{spheical-coordinates-int}
|
||||
\desc{Integration in spherical coordinates}{}{}
|
||||
\desc[german]{Integration in Kugelkoordinaten}{}{}
|
||||
@ -260,6 +281,40 @@
|
||||
\eq{\zeta(s) = \sum_{n=1}^{\infty} \frac{1}{n^s} = \frac{1}{(1-2^{(1-s)})\Gamma(s)} \int_0^\infty \d\eta \frac{\eta^{(s-1)}}{\e^\eta + 1}}
|
||||
\end{formula}
|
||||
|
||||
\begin{formula}{gamma_function}
|
||||
\desc{Gamma function}{}{}
|
||||
\desc[german]{Gamma-Funktion}{}{}
|
||||
\eq{
|
||||
\Gamma(n) &= (n-1)! \\
|
||||
\Gamma(z) &= \int_0^\infty t^{z-1} \e^{-t} \d t \\
|
||||
\Gamma(z+1) &= z\Gamma(z)
|
||||
}
|
||||
\end{formula}
|
||||
\begin{formula}{upper_incomplete_gamma_function}
|
||||
\desc{Upper incomplete gamma function}{}{}
|
||||
\desc[german]{Unvollständige Gamma-Funktion der unteren Grenze}{}{}
|
||||
\eq{\Gamma(s,x) = \int_x-^\infty t^{s-1}\e^{-t} \d t}
|
||||
\end{formula}
|
||||
\begin{formula}{lower_incomplete_gamma_function}
|
||||
\desc{Lower incomplete gamma function}{}{}
|
||||
\desc[german]{Unvollständige Gamma-Funktion der oberen Grenze}{}{}
|
||||
\eq{\gamma(s,x) = \int_0^x t^{s-1}\e^{-t} \d t}
|
||||
\end{formula}
|
||||
|
||||
\begin{formula}{beta_function}
|
||||
\desc{Beta function}{Complete beta function}{}
|
||||
\desc[german]{Beta-Funktion}{}{}
|
||||
\eq{
|
||||
\txB(z_1,z_2) &= \int_0^1 t^{z_1-1} (1-t)^{z_2-1} \d t \\
|
||||
\txB(z_1, z_2) &= \frac{\Gamma(z_1) \Gamma(z_2)}{\Gamma(z_1+z_2)}
|
||||
}
|
||||
\end{formula}
|
||||
\begin{formula}{incomplete_beta_function}
|
||||
\desc{Incomplete beta function}{Complete beta function}{}
|
||||
\desc[german]{Unvollständige Beta-Funktion}{}{}
|
||||
\eq{\txB(x; z_1,z_2) = \int_0^x t^{z_1-1} (1-t)^{z_2-1} \d t}
|
||||
\end{formula}
|
||||
|
||||
|
||||
\TODO{differential equation solutions}
|
||||
|
||||
|
||||
@ -9,6 +9,7 @@
|
||||
\eq{\braket{x} = \int w(x)\, x\, \d x}
|
||||
\end{formula}
|
||||
|
||||
|
||||
\begin{formula}{variance}
|
||||
\desc{Variance}{Square of the \fqEqRef{math:pt:std-deviation}}{}
|
||||
\desc[german]{Varianz}{Quadrat der\fqEqRef{math:pt:std-deviation}}{}
|
||||
@ -47,35 +48,51 @@
|
||||
\eq{F(x) = \int_{-\infty}^x f(t) \d t}
|
||||
\end{formula}
|
||||
|
||||
\begin{formula}{pmf}
|
||||
\desc{Probability mass function}{Probability $p$ that \textbf{discrete} random variable $X$ has exact value $x$}{$P$ probability measure}
|
||||
\desc[german]{Wahrscheinlichkeitsfunktion / Zählfunktion}{Wahrscheinlichkeit $p$ dass eine \textbf{diskrete} Zufallsvariable $X$ einen exakten Wert $x$ annimmt}{}
|
||||
\eq{p_X(x) = P(X = x)}
|
||||
\end{formula}
|
||||
|
||||
\begin{formula}{autocorrelation}
|
||||
\desc{Autocorrelation}{Correlation of $f$ to itself at an earlier point in time, $C$ is a covariance function}{}
|
||||
\desc[german]{Autokorrelation}{Korrelation vonn $f$ zu sich selbst zu einem früheren Zeitpunkt. $C$ ist auch die Kovarianzfunktion}{}
|
||||
\eq{C_A(\tau) = \lim_{T \to \infty} \frac{1}{2T}\int_{-T}^{T} f(t+\tau) f(t) \d t) = \braket{f(t+\tau)\cdot f(t)}}
|
||||
\end{formula}
|
||||
|
||||
\begin{formula}{binomial_coefficient}
|
||||
\desc{Binomial coefficient}{Number of possibilitites of choosing $k$ objects out of $n$ objects\\}{}
|
||||
\desc[german]{Binomialkoeffizient}{Anzahl der Möglichkeiten, $k$ aus $n$ zu wählen\\ "$n$ über $k$"}{}
|
||||
\eq{\binom{n}{k} = \frac{n!}{k!(n-k)!}}
|
||||
\end{formula}
|
||||
|
||||
\Subsection[
|
||||
\eng{Distributions}
|
||||
\ger{Verteilungen}
|
||||
]{distributions}
|
||||
\Subsubsection[
|
||||
\eng{Gauß/Normal distribution}
|
||||
\ger{Gauß/Normal-Verteilung}
|
||||
]{normal}
|
||||
\begin{minipage}{\distleftwidth}
|
||||
\begin{figure}[H]
|
||||
\centering
|
||||
\includegraphics[width=\textwidth]{img/distribution_gauss.pdf}
|
||||
\end{figure}
|
||||
\end{minipage}
|
||||
\begin{distribution}
|
||||
\disteq{parameters}{\mu \in \R,\quad \sigma^2 \in \R}
|
||||
\disteq{support}{x \in \R}
|
||||
\disteq{pdf}{\frac{1}{\sqrt{2\pi\sigma^2}}\exp \left(-\frac{(x-\mu)^2}{2\sigma^2}\right)}
|
||||
\disteq{cdf}{\frac{1}{2}\left[1 + \erf \left(\frac{x-\mu}{\sqrt{2}\sigma}\right)\right]}
|
||||
\disteq{mean}{\mu}
|
||||
\disteq{median}{\mu}
|
||||
\disteq{variance}{\sigma^2}
|
||||
\end{distribution}
|
||||
\eng{Continuous probability distributions}
|
||||
\ger{Kontinuierliche Wahrscheinlichkeitsverteilungen}
|
||||
]{cont}
|
||||
\begin{bigformula}{normal}
|
||||
\desc{Gauß/Normal distribution}{}{}
|
||||
\desc[german]{Gauß/Normal-Verteilung}{}{}
|
||||
\begin{minipage}{\distleftwidth}
|
||||
\begin{figure}[H]
|
||||
\centering
|
||||
\includegraphics[width=\textwidth]{img/distribution_gauss.pdf}
|
||||
\end{figure}
|
||||
\end{minipage}
|
||||
\begin{distribution}
|
||||
\disteq{parameters}{\mu \in \R,\quad \sigma^2 \in \R}
|
||||
\disteq{support}{x \in \R}
|
||||
\disteq{pdf}{\frac{1}{\sqrt{2\pi\sigma^2}}\exp \left(-\frac{(x-\mu)^2}{2\sigma^2}\right)}
|
||||
\disteq{cdf}{\frac{1}{2}\left[1 + \erf \left(\frac{x-\mu}{\sqrt{2}\sigma}\right)\right]}
|
||||
\disteq{mean}{\mu}
|
||||
\disteq{median}{\mu}
|
||||
\disteq{variance}{\sigma^2}
|
||||
\end{distribution}
|
||||
\end{bigformula}
|
||||
|
||||
\begin{formula}{standard_normal_distribution}
|
||||
\desc{Density function of the standard normal distribution}{$\mu = 0$, $\sigma = 1$}{}
|
||||
@ -83,98 +100,138 @@
|
||||
\eq{\varphi(x) = \frac{1}{\sqrt{2\pi}} \e^{-\frac{1}{2}x^2}}
|
||||
\end{formula}
|
||||
|
||||
\Subsubsection[
|
||||
\eng{Cauchys / Lorentz distribution}
|
||||
\ger{Cauchy / Lorentz-Verteilung}
|
||||
]{cauchy}
|
||||
\begin{minipage}{\distleftwidth}
|
||||
\begin{figure}[H]
|
||||
\centering
|
||||
\includegraphics[width=\textwidth]{img/distribution_cauchy.pdf}
|
||||
\end{figure}
|
||||
\end{minipage}
|
||||
\begin{distribution}
|
||||
\disteq{parameters}{x_0 \in \R,\quad \gamma \in \R}
|
||||
\disteq{support}{x \in \R}
|
||||
\disteq{pdf}{\frac{1}{\pi\gamma\left[1+\left(\frac{x-x_0}{\gamma}\right)^2\right]}}
|
||||
\disteq{cdf}{\frac{1}{\pi}\arctan\left(\frac{x-x_0}{\gamma}\right) + \frac{1}{2}}
|
||||
\disteq{mean}{\text{\GT{undefined}}}
|
||||
\disteq{median}{x_0}
|
||||
\disteq{variance}{\text{\GT{undefined}}}
|
||||
\end{distribution}
|
||||
\noindent
|
||||
\begin{ttext}
|
||||
\eng{Also known as \textbf{Cauchy-Lorentz distribution}, \textbf{Lorentz(ian) function}, \textbf{Breit-Wigner distribution}.}
|
||||
\ger{Auch bekannt als \textbf{Cauchy-Lorentz Verteilung}, \textbf{Lorentz Funktion}, \textbf{Breit-Wigner Verteilung}.}
|
||||
\end{ttext}
|
||||
\begin{bigformula}{cauchy}
|
||||
\desc{Cauchys / Lorentz distribution}{Also known as Cauchy-Lorentz distribution, Lorentz(ian) function, Breit-Wigner distribution.}{}
|
||||
\desc[german]{Cauchy / Lorentz-Verteilung}{Auch bekannt als Cauchy-Lorentz Verteilung, Lorentz Funktion, Breit-Wigner Verteilung.}{}
|
||||
\begin{minipage}{\distleftwidth}
|
||||
\begin{figure}[H]
|
||||
\centering
|
||||
\includegraphics[width=\textwidth]{img/distribution_cauchy.pdf}
|
||||
\end{figure}
|
||||
\end{minipage}
|
||||
\begin{distribution}
|
||||
\disteq{parameters}{x_0 \in \R,\quad \gamma \in \R}
|
||||
\disteq{support}{x \in \R}
|
||||
\disteq{pdf}{\frac{1}{\pi\gamma\left[1+\left(\frac{x-x_0}{\gamma}\right)^2\right]}}
|
||||
\disteq{cdf}{\frac{1}{\pi}\arctan\left(\frac{x-x_0}{\gamma}\right) + \frac{1}{2}}
|
||||
\disteq{mean}{\text{\GT{undefined}}}
|
||||
\disteq{median}{x_0}
|
||||
\disteq{variance}{\text{\GT{undefined}}}
|
||||
\end{distribution}
|
||||
\end{bigformula}
|
||||
|
||||
\begin{bigformula}{maxwell-boltzmann}
|
||||
\desc{Maxwell-Boltzmann distribution}{}{}
|
||||
\desc[german]{Maxwell-Boltzmann Verteilung}{}{}
|
||||
\begin{minipage}{\distleftwidth}
|
||||
\begin{figure}[H]
|
||||
\centering
|
||||
\includegraphics[width=\textwidth]{img/distribution_maxwell-boltzmann.pdf}
|
||||
\end{figure}
|
||||
\end{minipage}
|
||||
\begin{distribution}
|
||||
\disteq{parameters}{a > 0}
|
||||
\disteq{support}{x \in (0, \infty)}
|
||||
\disteq{pdf}{\sqrt{\frac{2}{\pi}} \frac{x^2}{a^3} \exp\left(-\frac{x^2}{2a^2}\right)}
|
||||
\disteq{cdf}{\erf \left(\frac{x}{\sqrt{2} a}\right) - \sqrt{\frac{2}{\pi}} \frac{x}{a} \exp\left({\frac{-x^2}{2a^2}}\right)}
|
||||
\disteq{mean}{2a \frac{2}{\pi}}
|
||||
\disteq{median}{}
|
||||
\disteq{variance}{\frac{a^2(3\pi-8)}{\pi}}
|
||||
\end{distribution}
|
||||
\end{bigformula}
|
||||
|
||||
|
||||
\begin{bigformula}{gamma}
|
||||
\desc{Gamma Distribution}{with $\lambda$ parameter}{$\Gamma$ \fqEqRef{math:cal:integral:list:gamma}, $\gamma$ \fqEqRef{math:cal:integral:list:lower_incomplete_gamma_function}}
|
||||
\desc[german]{Gamma Verteilung}{mit $\lambda$ Parameter}{}
|
||||
\begin{minipage}{\distleftwidth}
|
||||
\begin{figure}[H]
|
||||
\centering
|
||||
\includegraphics[width=\textwidth]{img/distribution_gamma.pdf}
|
||||
\end{figure}
|
||||
\end{minipage}
|
||||
\begin{distribution}
|
||||
\disteq{parameters}{\alpha > 0, \lambda > 0}
|
||||
\disteq{support}{x\in(0,1)}
|
||||
\disteq{pdf}{\frac{\lambda^\alpha}{\Gamma(\alpha) x^{\alpha-1} \e^{-\lambda x}}}
|
||||
\disteq{cdf}{\frac{1}{\Gamma(\alpha) \gamma(\alpha, \lambda x)}}
|
||||
\disteq{mean}{\frac{\alpha}{\lambda}}
|
||||
\disteq{variance}{\frac{\alpha}{\lambda^2}}
|
||||
\end{distribution}
|
||||
\end{bigformula}
|
||||
|
||||
\begin{bigformula}{beta}
|
||||
\desc{Beta Distribution}{}{$\txB$ \fqEqRef{math:cal:integral:list:beta_function} / \fqEqRef{math:cal:integral:list:incomplete_beta_function}}
|
||||
\desc[german]{Beta Verteilung}{}{}
|
||||
\begin{minipage}{\distleftwidth}
|
||||
\begin{figure}[H]
|
||||
\centering
|
||||
\includegraphics[width=\textwidth]{img/distribution_beta.pdf}
|
||||
\end{figure}
|
||||
\end{minipage}
|
||||
\begin{distribution}
|
||||
\disteq{parameters}{\alpha \in \R, \beta \in \R}
|
||||
\disteq{support}{x\in[0,1]}
|
||||
\disteq{pdf}{\frac{x^{\alpha-1} (1-x)^{\beta-1}}{\txB(\alpha,\beta)}}
|
||||
\disteq{cdf}{\frac{\txB(x;\alpha,\beta)}{\txB(\alpha,\beta)}}
|
||||
\disteq{mean}{\frac{\alpha}{\alpha+\beta}}
|
||||
% \disteq{median}{\frac{}{}} % pretty complicated, probably not needed
|
||||
\disteq{variance}{\frac{\alpha\beta}{(\alpha+\beta)^2(\alpha+\beta+1)}}
|
||||
\end{distribution}
|
||||
\end{bigformula}
|
||||
|
||||
|
||||
\Subsubsection[
|
||||
\eng{Binomial distribution}
|
||||
\ger{Binomialverteilung}
|
||||
]{binomial}
|
||||
\begin{ttext}
|
||||
\eng{For the number of trials going to infinity ($n\to\infty$), the binomial distribution converges to the \hyperref[sec:pb:distributions:poisson]{poisson distribution}}
|
||||
\ger{Geht die Zahl der Versuche gegen unendlich ($n\to\infty$), konvergiert die Binomualverteilung gegen die \hyperref[sec:pb:distributions:poisson]{Poissonverteilung}}
|
||||
\end{ttext}\\
|
||||
\begin{minipage}{\distleftwidth}
|
||||
\begin{figure}[H]
|
||||
\centering
|
||||
\includegraphics[width=\textwidth]{img/distribution_binomial.pdf}
|
||||
\end{figure}
|
||||
\end{minipage}
|
||||
\begin{distribution}
|
||||
\disteq{parameters}{n \in \Z, \quad p \in [0,1],\quad q = 1 - p}
|
||||
\disteq{support}{k \in \{0,\,1,\,\dots,\,n\}}
|
||||
\disteq{pmf}{\binom{n}{k} p^k q^{n-k}}
|
||||
% \disteq{cdf}{\text{regularized incomplete beta function}}
|
||||
\disteq{mean}{np}
|
||||
\disteq{median}{\floor{np} \text{ or } \ceil{np}}
|
||||
\disteq{variance}{npq = np(1-p)}
|
||||
\end{distribution}
|
||||
\Subsubsection[
|
||||
\eng{Poisson distribution}
|
||||
\ger{Poissonverteilung}
|
||||
]{poisson}
|
||||
\begin{minipage}{\distleftwidth}
|
||||
\begin{figure}[H]
|
||||
\centering
|
||||
\includegraphics[width=\textwidth]{img/distribution_poisson.pdf}
|
||||
\end{figure}
|
||||
\end{minipage}
|
||||
\begin{distribution}
|
||||
\disteq{parameters}{\lambda \in (0,\infty)}
|
||||
\disteq{support}{k \in \N}
|
||||
\disteq{pmf}{\frac{\lambda^k \e^{-\lambda}}{k!}}
|
||||
\disteq{cdf}{\e^{-\lambda} \sum_{j=0}^{\floor{k}} \frac{\lambda^j}{j!}}
|
||||
\disteq{mean}{\lambda}
|
||||
\disteq{median}{\approx\floor*{\lambda + \frac{1}{3} - \frac{1}{50\lambda}}}
|
||||
\disteq{variance}{\lambda}
|
||||
\end{distribution}
|
||||
|
||||
\eng{Discrete probability distributions}
|
||||
\ger{Diskrete Wahrscheinlichkeitsverteilungen}
|
||||
]{discrete}
|
||||
\begin{bigformula}{binomial}
|
||||
\desc{Binomial distribution}{}{}
|
||||
\desc[german]{Binomialverteilung}{}{}
|
||||
\begin{ttext}
|
||||
\eng{For the number of trials going to infinity ($n\to\infty$), the binomial distribution converges to the \hyperref[sec:pb:distributions:poisson]{poisson distribution}}
|
||||
\ger{Geht die Zahl der Versuche gegen unendlich ($n\to\infty$), konvergiert die Binomualverteilung gegen die \hyperref[sec:pb:distributions:poisson]{Poissonverteilung}}
|
||||
\end{ttext}\\
|
||||
\begin{minipage}{\distleftwidth}
|
||||
\begin{figure}[H]
|
||||
\centering
|
||||
\includegraphics[width=\textwidth]{img/distribution_binomial.pdf}
|
||||
\end{figure}
|
||||
\end{minipage}
|
||||
\begin{distribution}
|
||||
\disteq{parameters}{n \in \Z, \quad p \in [0,1],\quad q = 1 - p}
|
||||
\disteq{support}{k \in \{0,\,1,\,\dots,\,n\}}
|
||||
\disteq{pmf}{\binom{n}{k} p^k q^{n-k}}
|
||||
% \disteq{cdf}{\text{regularized incomplete beta function}}
|
||||
\disteq{mean}{np}
|
||||
\disteq{median}{\floor{np} \text{ or } \ceil{np}}
|
||||
\disteq{variance}{npq = np(1-p)}
|
||||
\end{distribution}
|
||||
\end{bigformula}
|
||||
|
||||
\Subsubsection[
|
||||
\eng{Maxwell-Boltzmann distribution}
|
||||
\ger{Maxwell-Boltzmann Verteilung}
|
||||
]{maxwell-boltzmann}
|
||||
\begin{minipage}{\distleftwidth}
|
||||
\begin{figure}[H]
|
||||
\centering
|
||||
\includegraphics[width=\textwidth]{img/distribution_maxwell-boltzmann.pdf}
|
||||
\end{figure}
|
||||
\end{minipage}
|
||||
\begin{distribution}
|
||||
\disteq{parameters}{a > 0}
|
||||
\disteq{support}{x \in (0, \infty)}
|
||||
\disteq{pdf}{\sqrt{\frac{2}{\pi}} \frac{x^2}{a^3} \exp\left(-\frac{x^2}{2a^2}\right)}
|
||||
\disteq{cdf}{\erf \left(\frac{x}{\sqrt{2} a}\right) - \sqrt{\frac{2}{\pi}} \frac{x}{a} \exp\left({\frac{-x^2}{2a^2}}\right)}
|
||||
\disteq{mean}{2a \frac{2}{\pi}}
|
||||
\disteq{median}{}
|
||||
\disteq{variance}{\frac{a^2(3\pi-8)}{\pi}}
|
||||
\end{distribution}
|
||||
\begin{bigformula}{poisson}
|
||||
\desc{Poisson distribution}{}{}
|
||||
\desc[german]{Poissonverteilung}{}{}
|
||||
\begin{minipage}{\distleftwidth}
|
||||
\begin{figure}[H]
|
||||
\centering
|
||||
\includegraphics[width=\textwidth]{img/distribution_poisson.pdf}
|
||||
\end{figure}
|
||||
\end{minipage}
|
||||
\begin{distribution}
|
||||
\disteq{parameters}{\lambda \in (0,\infty)}
|
||||
\disteq{support}{k \in \N}
|
||||
\disteq{pmf}{\frac{\lambda^k \e^{-\lambda}}{k!}}
|
||||
\disteq{cdf}{\e^{-\lambda} \sum_{j=0}^{\floor{k}} \frac{\lambda^j}{j!}}
|
||||
\disteq{mean}{\lambda}
|
||||
\disteq{median}{\approx\floor*{\lambda + \frac{1}{3} - \frac{1}{50\lambda}}}
|
||||
\disteq{variance}{\lambda}
|
||||
\end{distribution}
|
||||
\end{bigformula}
|
||||
|
||||
|
||||
|
||||
% TEMPLATE
|
||||
% \begin{distribution}{maxwell-boltzmann}
|
||||
% \distdesc{Maxwell-Boltzmann distribution}{}
|
||||
% \distdesc[german]{Maxwell-Boltzmann Verteilung}{}
|
||||
@ -238,4 +295,51 @@
|
||||
\eq{\sigma^2_{\overline{x}} = \frac{1}{\sum_i w_i}}
|
||||
\end{formula}
|
||||
|
||||
\Subsection[
|
||||
\eng{Maximum likelihood estimation}
|
||||
\ger{Maximum likelihood Methode}
|
||||
]{mle}
|
||||
\begin{formula}{likelihood}
|
||||
\desc{Likelihood function}{Likelihood of observing $x$ when parameter is $\theta$\\in general not normalized!}{$\rho$ \fqEqRef{math:pt:pdf} $x\mapsto \rho(x|\theta)$ depending on parameter $\theta$, $\Theta$ parameter space}
|
||||
\desc[german]{Likelihood Funktion}{"Plausibilität" $x$ zu messen, wenn der Parameter $\theta$ ist\\nicht normalisiert!}{$\rho$ \fqEqRef{math:pt:pdf} $x\mapsto \rho(x|\theta)$ hängt ab von Parameter $\theta$, $\Theta$ Parameterraum}
|
||||
\eq{L:\Theta \rightarrow [0,1], \quad \theta \mapsto \rho(x|\theta)}
|
||||
\end{formula}
|
||||
\begin{formula}{likelihood_independant}
|
||||
\desc{Likelihood function}{for independent and identically distributed random variables}{$x_i$ $n$ random variables, $\rho$ \fqEqRef{math:pt:pdf} $x\mapsto \rho(x|\theta)$ depending on parameter $\theta$}
|
||||
\desc[german]{Likelihood function}{für unabhängig und identisch verteilte Zufallsvariablen}{$x_i$ $n$ Zufallsvariablen$\rho$ \fqEqRef{math:pt:pdf} $x\mapsto \rho(x|\theta)$ hängt ab von Parameter $\theta$}
|
||||
\eq{L(\theta) = \prod_{i=1}^n f(x_i;\theta)}
|
||||
\end{formula}
|
||||
\begin{formula}{maximum_likelihood_estimate}
|
||||
\desc{Maximum likelihood estimate (MLE)}{Paramater for which outcome is most likely}{$L$ \fqEqRef{pt:mle:likelihood}, $\theta$ parameter of a \fqEqRef{math:pt:pdf}}
|
||||
\desc[german]{Maximum likelihood-Schätzung (MLE)}{Paramater, für den das Ergebnis am Wahrscheinlichsten ist}{$L$ \fqEqRef{math:pt:mle:likelihood}, $\theta$ Parameter einer \fqEqRef{math:pt:pdf}}
|
||||
\eq{\theta_\text{ML} &= \argmax_\theta L(\theta)\\ &= \argmax_\theta \log \big(L(\theta)\big)}
|
||||
\end{formula}
|
||||
|
||||
\Subsection[
|
||||
\eng{Bayesian probability theory}
|
||||
\ger{Bayessche Wahrscheinlichkeitstheorie}
|
||||
]{bayesian}
|
||||
\begin{formula}{prior}
|
||||
\desc{Prior distribution}{Expected distribution before conducting the experiment}{$\theta$ parameter}
|
||||
\desc[german]{Prior Verteilung}{}{}
|
||||
\eq{p(\theta)}
|
||||
\end{formula}
|
||||
|
||||
\begin{formula}{evidence}
|
||||
\desc{Evidence}{}{$p(\mathcal{D}|\theta)$ \fqEqRef{math:pt:mle:likelihood}, $p(\theta)$ \fqEqRef{math:pt:bayesian:prior}, $\mathcal{D}$ data set}
|
||||
% \desc[german]{}{}{}
|
||||
\eq{p(\mathcal{D}) = \int\d\theta \,p(\mathcal{D}|\theta)\,p(\theta)}
|
||||
\end{formula}
|
||||
|
||||
\begin{formula}{theorem}
|
||||
\desc{Bayes' theorem}{}{$p(\theta|\mathcal{D})$ posterior distribution, $p(\mathcal{D}|\theta)$ \fqEqRef{math:pt:mle:likelihood}, $p(\theta)$ \fqEqRef{math:pt:bayesian:prior}, $p(\mathcal{D})$ \fqEqRef{math:pt:bayesian:evidence}, $\mathcal{D}$ data set}
|
||||
\desc[german]{Satz von Bayes}{}{}
|
||||
\eq{p(\theta|\mathcal{D}) = \frac{p(\mathcal{D}|\theta)\,p(\theta)}{p(\mathcal{D})}}
|
||||
\end{formula}
|
||||
|
||||
\begin{formula}{map}
|
||||
\desc{Maximum a posterior estimation (MAP)}{}{}
|
||||
% \desc[german]{}{}{}
|
||||
\eq{\theta_\text{MAP} = \argmax_\theta p(\theta|\mathcal{D}) = \argmax_\theta p(\mathcal{D}|\theta)\,p(\theta)}
|
||||
\end{formula}
|
||||
|
||||
|
||||
@ -3,6 +3,34 @@
|
||||
\ger{Mechanik}
|
||||
]{mech}
|
||||
|
||||
\Section[
|
||||
\eng{Newton}
|
||||
\ger{Newton}
|
||||
]{newton}
|
||||
\begin{formula}{newton_laws}
|
||||
\desc{Newton's laws}{}{}
|
||||
\desc[german]{Newtonsche Gesetze}{}{}
|
||||
\ttxt{
|
||||
\eng{
|
||||
\begin{enumerate}
|
||||
\item A body remains at rest, or in motion at a constant speed in a straight line, except insofar as it is acted upon by a force
|
||||
\item $$\vec{F} = m \cdot \vec{a}$$
|
||||
\item If two bodies exert forces on each other, these force have the same magnitude but opposite directions
|
||||
$$\vec{F}_{\txA\rightarrow\txB} = -\vec{F}_{\txB\rightarrow\txA}$$
|
||||
\end{enumerate}
|
||||
|
||||
}
|
||||
\ger{
|
||||
\begin{enumerate}
|
||||
\item Ein kräftefreier Körper bleibt in Ruhe oder bewegt sich geradlinig mit konstanter Geschwindigkeit
|
||||
\item $$\vec{F} = m \cdot \vec{a}$$
|
||||
\item Eine Kraft von Körper A auf Körper B geht immer mit einer gleich große, aber entgegen gerichteten Kraft von Körper B auf Körper A einher:
|
||||
$$\vec{F}_{\txA\rightarrow\txB} = -\vec{F}_{\txB\rightarrow\txA}$$
|
||||
\end{enumerate}
|
||||
}
|
||||
}
|
||||
\end{formula}
|
||||
|
||||
\Section[
|
||||
\eng{Misc}
|
||||
\ger{Verschiedenes}
|
||||
|
||||
101
src/particle.tex
Normal file
101
src/particle.tex
Normal file
@ -0,0 +1,101 @@
|
||||
\Part[
|
||||
\eng{Particle physics}
|
||||
\ger{Teilchenphysik}
|
||||
]{particle}
|
||||
|
||||
\begin{formula}{electron_mass}
|
||||
\desc{Electron mass}{}{}
|
||||
\desc[german]{Elektronenmasse}{}{}
|
||||
\constant{m_\txe}{exp}{
|
||||
\val{9.1093837139(28) \xE{-31}}{\kg}
|
||||
}
|
||||
\end{formula}
|
||||
|
||||
\tikzset{%
|
||||
label/.style = { black, midway, align=center },
|
||||
toplabel/.style = { label, above=.5em, anchor=south },
|
||||
leftlabel/.style = { midway, left=.5em, anchor=east },
|
||||
bottomlabel/.style = { label, below=.5em, anchor=north },
|
||||
force/.style = { rotate=-90,scale=0.4 },
|
||||
round/.style = { rounded corners=2mm },
|
||||
legend/.style = { anchor=east },
|
||||
nosep/.style = { inner sep=0pt },
|
||||
generation/.style = { anchor=base },
|
||||
brace/.style = { decoration={brace,mirror},decorate }
|
||||
}
|
||||
|
||||
% [1]: color
|
||||
% 2: symbol
|
||||
% 3: name
|
||||
% 4: mass
|
||||
% 5: spin
|
||||
% 6: charge
|
||||
% 7: colors
|
||||
\newcommand\drawParticle[7][white]{%
|
||||
\begin{tikzpicture}[x=2.2cm, y=2.2cm]
|
||||
% \path[fill=#1,blur shadow={shadow blur steps=5}] (0,0) -- (1,0) -- (1,1) -- (0,1) -- cycle;
|
||||
% \path[fill=#1,stroke=black,blur shadow={shadow blur steps=5},rounded corners] (0,0) rectangle (1,1);
|
||||
\path[fill=#1!20!bg0,draw=#1,thick] (0.02,0.02) rectangle (0.98,0.98);
|
||||
\node at(0.92, 0.50) [nosep,anchor=east]{\Large #2};
|
||||
% \node at(0.95, 0.15) [nosep,anchor=south east]{\footnotesize #3};
|
||||
\node at(0.05, 0.15) [nosep,anchor=south west]{\footnotesize #3};
|
||||
% \ifstrempty{#2}{}{\node at(0) [nosep,anchor=west,scale=1.5] {#2};}
|
||||
% \ifstrempty{#3}{}{\node at(0.1,-0.85) [nosep,anchor=west,scale=0.3] {#3};}
|
||||
\ifstrempty{#4}{}{\node at(0.05,0.85) [nosep,anchor=west] {\footnotesize #4};}
|
||||
\ifstrempty{#5}{}{\node at(0.05,0.70) [nosep,anchor=west] {\footnotesize #5};}
|
||||
\ifstrempty{#6}{}{\node at(0.05,0.55) [nosep,anchor=west] {\footnotesize #6};}
|
||||
% \ifstrempty{#7}{}{\node at(0.05,0.40) [nosep,anchor=west] {\footnotesize #7};}
|
||||
\end{tikzpicture}
|
||||
}
|
||||
\def\colorLepton{bg-aqua}
|
||||
\def\colorQuarks{bg-purple}
|
||||
\def\colorGauBos{bg-red}
|
||||
\def\colorScaBos{bg-yellow}
|
||||
\eng[quarks]{Quarks}
|
||||
\ger[quarks]{Quarks}
|
||||
\eng[leptons]{Leptons}
|
||||
\ger[leptons]{Leptonen}
|
||||
\eng[fermions]{Fermions}
|
||||
\ger[fermions]{Fermionen}
|
||||
\eng[bosons]{Bosons}
|
||||
\ger[bosons]{Bosonen}
|
||||
|
||||
\begin{tikzpicture}[x=2.2cm, y=2.2cm]
|
||||
\node at(0, 0) {\drawParticle[\colorQuarks]{$u$} {up} {$2.3$ MeV}{1/2}{$2/3$}{R/G/B}};
|
||||
\node at(0,-1) {\drawParticle[\colorQuarks]{$d$} {down} {$4.8$ MeV}{1/2}{$-1/3$}{R/G/B}};
|
||||
\node at(0,-2) {\drawParticle[\colorLepton]{$e$} {electron} {$511$ keV}{1/2}{$-1$}{}};
|
||||
\node at(0,-3) {\drawParticle[\colorLepton]{$\nu_e$} {$e$ neutrino} {$<2.2$ eV}{1/2}{0}{}};
|
||||
\node at(1, 0) {\drawParticle[\colorQuarks]{$c$} {charm} {$1.275$ GeV}{1/2}{$2/3$}{R/G/B}};
|
||||
\node at(1,-1) {\drawParticle[\colorQuarks]{$s$} {strange} {$95$ MeV}{1/2}{$-1/3$}{R/G/B}};
|
||||
\node at(1,-2) {\drawParticle[\colorLepton]{$\mu$} {muon} {$105.7$ MeV}{1/2}{$-1$}{}};
|
||||
\node at(1,-3) {\drawParticle[\colorLepton]{$\nu_\mu$} {$\mu$ neutrino}{$<170$ keV}{1/2}{0}{}};
|
||||
\node at(2, 0) {\drawParticle[\colorQuarks]{$t$} {top} {$173.2$ GeV}{1/2}{$2/3$}{R/G/B}};
|
||||
\node at(2,-1) {\drawParticle[\colorQuarks]{$b$} {bottom} {$4.18$ GeV}{1/2}{$-1/3$}{R/G/B}};
|
||||
\node at(2,-2) {\drawParticle[\colorLepton]{$\tau$} {tau} {$1.777$ GeV}{1/2}{$-1$}{}};
|
||||
\node at(2,-3) {\drawParticle[\colorLepton]{$\nu_\tau$} {$\tau$ neutrino} {$<15.5$ MeV}{1/2}{0}{}};
|
||||
\node at(3, 0) {\drawParticle[\colorGauBos]{$g$} {gluon} {0}{1}{0}{color}};
|
||||
\node at(3,-1) {\drawParticle[\colorGauBos]{$\gamma$} {photon} {0}{1}{0}{}};
|
||||
\node at(3,-2) {\drawParticle[\colorGauBos]{$Z$} {} {$91.2$ GeV}{1}{0}{}};
|
||||
\node at(3,-3) {\drawParticle[\colorGauBos]{$W_\pm$} {} {$80.4$ GeV}{1}{$\pm1$}{}};
|
||||
\node at(4,0) {\drawParticle[\colorScaBos]{$H$} {Higgs} {$125.1$ GeV}{0}{0}{}};
|
||||
|
||||
\draw [->] (-0.7, 0.35) node [legend] {\qtyRef{mass}} -- (-0.5, 0.35);
|
||||
\draw [->] (-0.7, 0.20) node [legend] {\qtyRef{spin}} -- (-0.5, 0.20);
|
||||
\draw [->] (-0.7, 0.05) node [legend] {\qtyRef{charge}} -- (-0.5, 0.05);
|
||||
\draw [->] (-0.7,-0.10) node [legend] {\qtyRef{colors}} -- (-0.5,-0.10);
|
||||
|
||||
\draw [brace,draw=\colorQuarks] (-0.55, 0.5) -- (-0.55,-1.5) node[leftlabel,color=\colorQuarks] {\gt{quarks}};
|
||||
\draw [brace,draw=\colorLepton] (-0.55,-1.5) -- (-0.55,-3.5) node[leftlabel,color=\colorLepton] {\gt{leptons}};
|
||||
\draw [brace] (-0.5,-3.55) -- ( 2.5,-3.55) node[bottomlabel] {\gt{fermions}};
|
||||
\draw [brace] ( 2.5,-3.55) -- ( 4.5,-3.55) node[bottomlabel] {\gt{bosons}};
|
||||
|
||||
|
||||
\draw [brace] (0.5,0.55) -- (-0.5,0.55) node[toplabel] {\small standard matter};
|
||||
\draw [brace] (2.5,0.55) -- ( 0.5,0.55) node[toplabel] {\small unstable matter};
|
||||
\draw [brace] (4.5,0.55) -- ( 2.5,0.55) node[toplabel] {\small force carriers};
|
||||
|
||||
\node at (0,0.85) [generation] {\small I};
|
||||
\node at (1,0.85) [generation] {\small II};
|
||||
\node at (2,0.85) [generation] {\small III};
|
||||
\node at (1,1.05) [generation] {\small generation};
|
||||
\end{tikzpicture}
|
||||
@ -49,10 +49,36 @@
|
||||
\eq{E_n &= \frac{Z^2\mu e^4}{n^2(4\pi\epsilon_0)^2 2\hbar^2} = -E_\textrm{H}\frac{Z^2}{n^2}}
|
||||
\end{formula}
|
||||
|
||||
\begin{formula}{rydberg_constant_heavy}
|
||||
\desc{Rydberg constant}{for heavy atoms}{\ConstRef{electron_mass}, \ConstRef{elementary_charge}, \QtyRef{vacuum_permittivity}, \ConstRef{planck}, \ConstRef{vacuum_speed_of_light}}
|
||||
\desc[german]{Rydberg-Konstante}{für schwere Atome}{}
|
||||
\constant{R_\infty}{exp}{
|
||||
\val{10973731.568157(12)}{\per\m}
|
||||
}
|
||||
\eq{
|
||||
R_\infty = \frac{m_e e^4}{8\epsilon_0^2 h^3 c}
|
||||
}
|
||||
\end{formula}
|
||||
|
||||
\begin{formula}{rydberg_constant_corrected}
|
||||
\desc{Rydberg constant}{corrected for nucleus mass $M$}{\QtyRef{rydberg_constant_heavy}, $\mu = \left(\frac{1}{m_\txe} + \frac{1}{M}\right)^{-1}$ \GT{reduced_mass}, \ConstRef{electron_mass}}
|
||||
\desc[german]{Rydberg Konstante}{korrigiert für Kernmasse $M$}{}
|
||||
\eq{R_\txM = \frac{\mu}{m_\txe} R_\infty}
|
||||
\end{formula}
|
||||
|
||||
\begin{formula}{rydberg_energy}
|
||||
\desc{Rydberg energy}{}{}
|
||||
\desc[german]{Rydberg-Energy}{}{}
|
||||
\eq{E_\textrm{H} = h\,c\,R_\textrm{H} = \frac{\mu e^4}{(4\pi\epsilon_0)^2 2\hbar^2}}
|
||||
\desc{Rydberg energy}{Energy unit}{\ConstRef{rydberg_constant_heavy}, \ConstRef{planck}, \ConstRef{vacuum_speed_of_light}}
|
||||
\desc[german]{Rydberg-Energy}{Energie Einheit}{}
|
||||
\eq{1\,\text{Ry} = hc\,R_\infty}
|
||||
\end{formula}
|
||||
|
||||
\begin{formula}{bohr_radius}
|
||||
\desc{Bohr radius}{}{\ConstRef{vacuum_permittivity}, \ConstRef{electron_mass}}
|
||||
\desc[german]{Bohrscher Radius}{}{}
|
||||
\constant{a_0}{exp}{
|
||||
\val{5.29177210544(82) \xE{-11}}{\m}
|
||||
}
|
||||
\eq{a_0 = \frac{4\pi \epsilon_0 \hbar^2}{e^2 m_\txe}}
|
||||
\end{formula}
|
||||
|
||||
|
||||
@ -80,11 +80,12 @@
|
||||
\begin{formula}{pauli_matrices}
|
||||
\desc{Pauli matrices}{}{}
|
||||
\desc[german]{Pauli Matrizen}{}{}
|
||||
\eqAlignedAt{2}{
|
||||
\newFormulaEntry
|
||||
\begin{alignat}{2}
|
||||
\sigma_x &= \sigmaxmatrix &&= \sigmaxbraket \label{eq:pauli_x} \\
|
||||
\sigma_y &= \sigmaymatrix &&= \sigmaybraket \label{eq:pauli_y} \\
|
||||
\sigma_z &= \sigmazmatrix &&= \sigmazbraket \label{eq:pauli_z}
|
||||
}
|
||||
\end{alignat}
|
||||
\end{formula}
|
||||
% $\sigma_x$ NOT
|
||||
% $\sigma_y$ PHASE
|
||||
@ -177,7 +178,7 @@
|
||||
\Section[
|
||||
\eng{Schrödinger equation}
|
||||
\ger{Schrödingergleichung}
|
||||
]{schroedinger_equation}
|
||||
]{se}
|
||||
\begin{formula}{energy_operator}
|
||||
\desc{Energy operator}{}{}
|
||||
\desc[german]{Energieoperator}{}{}
|
||||
@ -338,7 +339,7 @@
|
||||
\desc{2. order energy shift}{}{}
|
||||
\desc[german]{Energieverschiebung 2. Ordnung}{}{}
|
||||
% \eq{E_n^{(1)} = \Braket{\psi_n^{(0)}|\hat{H_1}|\psi_n^{(0)}}}
|
||||
\eq{E_n^{(2)} = \sum_{k\neq n}\frac{\abs*{\Braket{\psi_k^{(0)}|\hat{H_1}|\psi_n^{(0)}}}^2}{E_n^{(0)} - E_k^{(0)}}}
|
||||
\eq{E_n^{(2)} = \sum_{k\neq n}\frac{\abs{\Braket{\psi_k^{(0)}|\hat{H_1}|\psi_n^{(0)}}}^2}{E_n^{(0)} - E_k^{(0)}}}
|
||||
\end{formula}
|
||||
% \begin{formula}{qm:pertubation:}
|
||||
% \desc{1. order states}{}{}
|
||||
@ -347,16 +348,16 @@
|
||||
% \end{formula}
|
||||
|
||||
\begin{formula}{golden_rule}
|
||||
\desc{Fermi\'s golden rule}{Transition rate from initial state $\ket{i}$ under a pertubation $H^1$ to final state $\ket{f}$}{}
|
||||
\desc{Fermi's golden rule}{Transition rate from initial state $\ket{i}$ under a pertubation $H^1$ to final state $\ket{f}$}{}
|
||||
\desc[german]{Fermis goldene Regel}{Übergangsrate des initial Zustandes $\ket{i}$ unter einer Störung $H^1$ zum Endzustand $\ket{f}$}{}
|
||||
\eq{\Gamma_{i\to f} = \frac{2\pi}{\hbar} \abs*{\braket{f | H^1 | i}}^2\,\rho(E_f)}
|
||||
\eq{\Gamma_{i\to f} = \frac{2\pi}{\hbar} \abs{\braket{f | H^1 | i}}^2\,\rho(E_f)}
|
||||
\end{formula}
|
||||
|
||||
|
||||
\Section[
|
||||
\eng{Harmonic oscillator}
|
||||
\ger{Harmonischer Oszillator}
|
||||
]{qm_hosc}
|
||||
]{hosc}
|
||||
\begin{formula}{hamiltonian}
|
||||
\desc{Hamiltonian}{}{}
|
||||
\desc[german]{Hamiltonian}{}{}
|
||||
@ -18,7 +18,7 @@
|
||||
\quantity{t}{\second}{}
|
||||
\end{formula}
|
||||
|
||||
\begin{formula}{Length}
|
||||
\begin{formula}{length}
|
||||
\desc{Length}{}{}
|
||||
\desc[german]{Länge}{}{}
|
||||
\quantity{l}{\m}{e}
|
||||
@ -58,7 +58,6 @@
|
||||
\eng{Mechanics}
|
||||
\ger{Mechanik}
|
||||
]{mech}
|
||||
|
||||
\begin{formula}{force}
|
||||
\desc{Force}{}{}
|
||||
\desc[german]{Kraft}{}{}
|
||||
@ -107,13 +106,42 @@
|
||||
\desc[german]{Ladung}{}{}
|
||||
\quantity{q}{\coulomb=\ampere\s}{}
|
||||
\end{formula}
|
||||
\begin{formula}{charge_number}
|
||||
\desc{Charge number}{}{}
|
||||
\desc[german]{ladungszahl}{Anzahl der Elementarladungen}{}
|
||||
\quantity{Z}{}{}
|
||||
\end{formula}
|
||||
\begin{formula}{charge_density}
|
||||
\desc{Charge density}{}{}
|
||||
\desc[german]{Ladungsdichte}{}{}
|
||||
\quantity{\rho}{\coulomb\per\m^3}{s}
|
||||
\end{formula}
|
||||
|
||||
\begin{formula}{frequency}
|
||||
\desc{Frequency}{}{}
|
||||
\desc[german]{Frequenz}{}{}
|
||||
\quantity{f}{\hertz=\per\s}{s}
|
||||
\end{formula}
|
||||
\begin{formula}{angular_frequency}
|
||||
\desc{Angular frequency}{}{\QtyRef{time_period}, \QtyRef{frequency}}
|
||||
\desc[german]{Winkelgeschwindigkeit}{}{}
|
||||
\quantity{\omega}{\radian\per\s}{s}
|
||||
\eq{\omega = \frac{2\pi/T}{2\pi f}}
|
||||
\end{formula}
|
||||
|
||||
\begin{formula}{time_period}
|
||||
\desc{Time period}{}{\QtyRef{frequency}}
|
||||
\desc[german]{Periodendauer}{}{}
|
||||
\quantity{T}{\s}{s}
|
||||
\eq{T = \frac{1}{f}}
|
||||
\end{formula}
|
||||
|
||||
\Subsection[
|
||||
\eng{Others}
|
||||
\ger{Sonstige}
|
||||
]{other}
|
||||
\begin{formula}{area}
|
||||
\desc{Area}{}{}
|
||||
\desc[german]{Fläche}{}{}
|
||||
\quantity{A}{m^2}{v}
|
||||
\end{formula}
|
||||
|
||||
@ -24,12 +24,12 @@
|
||||
\begin{formula}{gates}
|
||||
\desc{}{}{}
|
||||
\desc[german]{}{}{}
|
||||
\eqAlignedAt{2}{
|
||||
\begin{alignat}{2}
|
||||
& \text{\gt{bitflip}:} & \hat{X} &= \sigma_x = \sigmaxmatrix \\
|
||||
& \text{\gt{bitphaseflip}:} & \hat{Y} &= \sigma_y = \sigmaymatrix \\
|
||||
& \text{\gt{phaseflip}:} & \hat{Z} &= \sigma_z = \sigmazmatrix \\
|
||||
& \text{\gt{hadamard}:} & \hat{H} &= \frac{1}{\sqrt{2}}(\hat{X}-\hat{Z}) = \begin{pmatrix} 1 & 1 \\ 1 & -1 \end{pmatrix}
|
||||
}
|
||||
\end{alignat}
|
||||
\end{formula}
|
||||
% \begin{itemize}
|
||||
% \item \gt{bitflip}: $\hat{X} = \sigma_x = \sigmaxmatrix$
|
||||
|
||||
@ -111,27 +111,32 @@
|
||||
\ger{Irreversible Gasexpansion (Gay-Lussac-Versuch)}
|
||||
]{gay}
|
||||
|
||||
\begin{minipage}{0.6\textwidth}
|
||||
\vfill
|
||||
\begin{ttext}
|
||||
\eng{
|
||||
A classical gas in a system with volume $V_1$ is separated from another system with volume $V_2$.
|
||||
In the Gay-Lussac experiment, the separation is removed and the gas flows into $V_2$.
|
||||
}
|
||||
\ger{
|
||||
Ein klassisches Gas in einem System mit Volumen $V_1$ ist getrennt von einem zweiten System mit Volumen $V_2$.
|
||||
Beim Gay-Lussac Versuch wird die Trennwand entfern und das Gas fließt in das Volumen $V_2$.
|
||||
}
|
||||
\end{ttext}
|
||||
\vfill
|
||||
\end{minipage}
|
||||
\hfill
|
||||
\begin{minipage}{0.3\textwidth}
|
||||
\begin{figure}[H]
|
||||
\centering
|
||||
\includegraphics[width=\textwidth]{img/td_gay_lussac.pdf}
|
||||
\end{figure}
|
||||
\end{minipage}
|
||||
\begin{bigformula}{experiment}
|
||||
\desc{Gay-Lussac experiment}{}{}
|
||||
\desc[german]{Gay-Lussac-Versuch}{}{}
|
||||
\begin{minipage}{0.6\textwidth}
|
||||
\vfill
|
||||
\begin{ttext}
|
||||
\eng{
|
||||
A classical gas in a system with volume $V_1$ is separated from another system with volume $V_2$.
|
||||
In the Gay-Lussac experiment, the separation is removed and the gas flows into $V_2$.
|
||||
}
|
||||
\ger{
|
||||
Ein klassisches Gas in einem System mit Volumen $V_1$ ist getrennt von einem zweiten System mit Volumen $V_2$.
|
||||
Beim Gay-Lussac Versuch wird die Trennwand entfern und das Gas fließt in das Volumen $V_2$.
|
||||
}
|
||||
\end{ttext}
|
||||
\vfill
|
||||
\end{minipage}
|
||||
\hfill
|
||||
\begin{minipage}{0.3\textwidth}
|
||||
\begin{figure}[H]
|
||||
\centering
|
||||
\includegraphics[width=\textwidth]{img/td_gay_lussac.pdf}
|
||||
\end{figure}
|
||||
\end{minipage}
|
||||
\end{bigformula}
|
||||
|
||||
|
||||
\begin{formula}{entropy}
|
||||
\desc{Entropy change}{}{}
|
||||
|
||||
0
src/svgs/convertToPdf.sh
Executable file → Normal file
0
src/svgs/convertToPdf.sh
Executable file → Normal file
11
src/test.tex
11
src/test.tex
@ -30,6 +30,17 @@ Is german? = \IfTranslation{german}{\ttest:name}{yes}{no} \\
|
||||
Is defined? = \IfTranslationExists{\ttest:name}{yes}{no} \\
|
||||
Is defined? = \expandafter\IfTranslationExists\expandafter{\ttest:name}{yes}{no}
|
||||
|
||||
\paragraph{Testing relative translations}
|
||||
\begingroup
|
||||
\edef\prevFqname{\fqname}
|
||||
\edef\fqname{\prevFqname:test}
|
||||
\eng{English, relative}
|
||||
\ger{Deutsch, relativ}
|
||||
\endgroup
|
||||
\dt[testkey]{english}{Testkey}
|
||||
{\textbackslash}gt\{test\}: \gt{test}\\
|
||||
{\textbackslash}gt\{test\}: \gt{testkey}
|
||||
|
||||
% \DT[qty:test]{english}{HAHA}
|
||||
|
||||
\paragraph{Testing hyperrefs}
|
||||
|
||||
37
src/util/colors.tex
Normal file
37
src/util/colors.tex
Normal file
@ -0,0 +1,37 @@
|
||||
|
||||
% \redefinecolor{black}{HTML}{fg0}
|
||||
% Dark mode
|
||||
\pagecolor{bg0}
|
||||
\color{fg0}
|
||||
|
||||
% \pagecolor{dark0_hard}
|
||||
% \color{light0_hard}
|
||||
|
||||
% section headings in bright colors, \titleformat from titlesec package
|
||||
\titleformat{\section}
|
||||
{\color{fg-purple}\normalfont\Large\bfseries}
|
||||
{\color{fg-purple}\thesection}{1em}{}
|
||||
|
||||
\titleformat{\subsection}
|
||||
{\color{fg-blue}\normalfont\large\bfseries}
|
||||
{\color{fg-blue}\thesubsection}{1em}{}
|
||||
|
||||
\titleformat{\subsubsection}
|
||||
{\color{fg-aqua}\normalfont\normalsize\bfseries}
|
||||
{\color{fg-aqua}\thesubsubsection}{1em}{}
|
||||
|
||||
\titleformat{\paragraph}
|
||||
{\color{fg-green}\normalfont\normalsize\bfseries}
|
||||
{\color{fg-green}\theparagraph}{1em}{}
|
||||
|
||||
\titleformat{\subparagraph}
|
||||
{\color{fg-purple}\normalfont\normalsize\bfseries}
|
||||
{\color{fg-purple}\thesubparagraph}{1em}{}
|
||||
|
||||
\hypersetup{
|
||||
colorlinks=true,
|
||||
linkcolor=fg-purple,
|
||||
citecolor=fg-green,
|
||||
filecolor=fg-blue,
|
||||
urlcolor=fg-orange
|
||||
}
|
||||
@ -1,72 +1,28 @@
|
||||
% Gruvbox colors
|
||||
\definecolor{dark0_hard}{HTML}{1d2021}
|
||||
\definecolor{dark0}{HTML}{282828}
|
||||
\definecolor{dark0_soft}{HTML}{32302f}
|
||||
\definecolor{dark1}{HTML}{3c3836}
|
||||
\definecolor{dark2}{HTML}{504945}
|
||||
\definecolor{dark3}{HTML}{665c54}
|
||||
\definecolor{dark4}{HTML}{7c6f64}
|
||||
\definecolor{medium}{HTML}{928374}
|
||||
\definecolor{light0_hard}{HTML}{f9f5d7}
|
||||
\definecolor{light0}{HTML}{fbf1c7}
|
||||
\definecolor{light0_soft}{HTML}{f2e5bc}
|
||||
\definecolor{light1}{HTML}{ebdbb2}
|
||||
\definecolor{light2}{HTML}{d5c4a1}
|
||||
\definecolor{light3}{HTML}{bdae93}
|
||||
\definecolor{light4}{HTML}{a89984}
|
||||
\definecolor{bright_red}{HTML}{fb4934}
|
||||
\definecolor{bright_green}{HTML}{b8bb26}
|
||||
\definecolor{bright_yellow}{HTML}{fabd2f}
|
||||
\definecolor{bright_blue}{HTML}{83a598}
|
||||
\definecolor{bright_purple}{HTML}{d3869b}
|
||||
\definecolor{bright_aqua}{HTML}{8ec07c}
|
||||
\definecolor{bright_orange}{HTML}{fe8019}
|
||||
\definecolor{neutral_red}{HTML}{cc241d}
|
||||
\definecolor{neutral_green}{HTML}{98971a}
|
||||
\definecolor{neutral_yellow}{HTML}{d79921}
|
||||
\definecolor{neutral_blue}{HTML}{458588}
|
||||
\definecolor{neutral_purple}{HTML}{b16286}
|
||||
\definecolor{neutral_aqua}{HTML}{689d6a}
|
||||
\definecolor{neutral_orange}{HTML}{d65d0e}
|
||||
\definecolor{faded_red}{HTML}{9d0006}
|
||||
\definecolor{faded_green}{HTML}{79740e}
|
||||
\definecolor{faded_yellow}{HTML}{b57614}
|
||||
\definecolor{faded_blue}{HTML}{076678}
|
||||
\definecolor{faded_purple}{HTML}{8f3f71}
|
||||
\definecolor{faded_aqua}{HTML}{427b58}
|
||||
\definecolor{faded_orange}{HTML}{af3a03}
|
||||
|
||||
% Dark mode
|
||||
% \pagecolor{light0_hard}
|
||||
% \color{dark0_hard}
|
||||
% \pagecolor{dark0_hard}
|
||||
% \color{light0_hard}
|
||||
|
||||
% section headings in bright colors, \titleformat from titlesec package
|
||||
\titleformat{\section}
|
||||
{\color{neutral_purple}\normalfont\Large\bfseries}
|
||||
{\color{neutral_purple}\thesection}{1em}{}
|
||||
|
||||
\titleformat{\subsection}
|
||||
{\color{neutral_blue}\normalfont\large\bfseries}
|
||||
{\color{neutral_blue}\thesubsection}{1em}{}
|
||||
|
||||
\titleformat{\subsubsection}
|
||||
{\color{neutral_aqua}\normalfont\normalsize\bfseries}
|
||||
{\color{neutral_aqua}\thesubsubsection}{1em}{}
|
||||
|
||||
\titleformat{\paragraph}
|
||||
{\color{neutral_green}\normalfont\normalsize\bfseries}
|
||||
{\color{neutral_green}\theparagraph}{1em}{}
|
||||
|
||||
\titleformat{\subparagraph}
|
||||
{\color{neutral_purple}\normalfont\normalsize\bfseries}
|
||||
{\color{neutral_purple}\thesubparagraph}{1em}{}
|
||||
|
||||
\hypersetup{
|
||||
colorlinks=true,
|
||||
linkcolor=neutral_purple,
|
||||
citecolor=neutral_green,
|
||||
filecolor=neutral_blue,
|
||||
urlcolor=neutral_orange
|
||||
}
|
||||
% This file was generated by scripts/formulasheet.py
|
||||
% Do not edit it directly, changes will be overwritten
|
||||
\definecolor{fg0}{HTML}{f9f5d7}
|
||||
\definecolor{bg0}{HTML}{1d2021}
|
||||
\definecolor{fg1}{HTML}{ebdbb2}
|
||||
\definecolor{fg2}{HTML}{d5c4a1}
|
||||
\definecolor{fg3}{HTML}{bdae93}
|
||||
\definecolor{fg4}{HTML}{a89984}
|
||||
\definecolor{bg1}{HTML}{3c3836}
|
||||
\definecolor{bg2}{HTML}{504945}
|
||||
\definecolor{bg3}{HTML}{665c54}
|
||||
\definecolor{bg4}{HTML}{7c6f64}
|
||||
\definecolor{fg-red}{HTML}{fb4934}
|
||||
\definecolor{fg-orange}{HTML}{f38019}
|
||||
\definecolor{fg-yellow}{HTML}{fabd2f}
|
||||
\definecolor{fg-green}{HTML}{b8bb26}
|
||||
\definecolor{fg-aqua}{HTML}{8ec07c}
|
||||
\definecolor{fg-blue}{HTML}{83a598}
|
||||
\definecolor{fg-purple}{HTML}{d3869b}
|
||||
\definecolor{fg-gray}{HTML}{a89984}
|
||||
\definecolor{bg-red}{HTML}{cc241d}
|
||||
\definecolor{bg-orange}{HTML}{d65d0e}
|
||||
\definecolor{bg-yellow}{HTML}{d79921}
|
||||
\definecolor{bg-green}{HTML}{98971a}
|
||||
\definecolor{bg-aqua}{HTML}{689d6a}
|
||||
\definecolor{bg-blue}{HTML}{458588}
|
||||
\definecolor{bg-purple}{HTML}{b16286}
|
||||
\definecolor{bg-gray}{HTML}{928374}
|
||||
|
||||
@ -15,6 +15,12 @@
|
||||
\def\descwidth{0.3\textwidth}
|
||||
\def\eqwidth{0.6\textwidth}
|
||||
|
||||
\newcommand\separateEntries{
|
||||
\vspace{0.5\baselineskip}
|
||||
\textcolor{fg3}{\hrule}
|
||||
\vspace{0.5\baselineskip}
|
||||
}
|
||||
|
||||
|
||||
%
|
||||
% FORMULA ENVIRONMENT
|
||||
@ -32,7 +38,7 @@
|
||||
\GT{#2}
|
||||
}{\detokenize{#2}}
|
||||
\IfTranslationExists{#3}{
|
||||
\\ {\color{dark1} \GT{#3}}
|
||||
\\ {\color{fg1} \GT{#3}}
|
||||
}{}
|
||||
\end{minipage}
|
||||
}
|
||||
@ -51,7 +57,7 @@
|
||||
\smartnewline
|
||||
\noindent
|
||||
\begingroup
|
||||
\color{dark1}
|
||||
\color{fg1}
|
||||
\GT{\ContentFqName}
|
||||
% \edef\temp{\GT{#1_defs}}
|
||||
% \expandafter\StrSubstitute\expandafter{\temp}{:}{\\}
|
||||
@ -90,7 +96,7 @@
|
||||
\newcommand{\eq}[1]{
|
||||
\newFormulaEntry
|
||||
\begin{align}
|
||||
\label{eq:\fqname:#1}
|
||||
% \label{eq:\fqname:#1}
|
||||
##1
|
||||
\end{align}
|
||||
}
|
||||
@ -175,17 +181,79 @@
|
||||
|
||||
\begingroup
|
||||
\label{f:\fqname:#1}
|
||||
\storeLabel{\fqname:#1}
|
||||
\par\noindent\ignorespaces
|
||||
% \textcolor{gray}{\hrule}
|
||||
\vspace{0.5\baselineskip}
|
||||
% \vspace{0.5\baselineskip}
|
||||
\NameWithDescription[\descwidth]{\fqname:#1}{\fqname:#1_desc}
|
||||
\hfill
|
||||
\begin{ContentBoxWithExplanation}{\fqname:#1_defs}
|
||||
}{
|
||||
\end{ContentBoxWithExplanation}
|
||||
\endgroup
|
||||
\textcolor{dark3}{\hrule}
|
||||
\vspace{0.5\baselineskip}
|
||||
\separateEntries
|
||||
% \textcolor{fg3}{\hrule}
|
||||
% \vspace{0.5\baselineskip}
|
||||
\ignorespacesafterend
|
||||
}
|
||||
|
||||
|
||||
% BIG FORMULA
|
||||
\newenvironment{bigformula}[1]{
|
||||
% [1]: language
|
||||
% 2: name
|
||||
% 3: description
|
||||
% 4: definitions/links
|
||||
\newcommand{\desc}[4][english]{
|
||||
% language, name, description, definitions
|
||||
\ifblank{##2}{}{\dt[#1]{##1}{##2}}
|
||||
\ifblank{##3}{}{\dt[#1_desc]{##1}{##3}}
|
||||
\ifblank{##4}{}{\dt[#1_defs]{##1}{##4}}
|
||||
}
|
||||
\directlua{n_formulaEntries = 0}
|
||||
\newcommand{\newFormulaEntry}{
|
||||
\directlua{
|
||||
if n_formulaEntries > 0 then
|
||||
tex.print("\\vspace{0.3\\baselineskip}\\hrule\\vspace{0.3\\baselineskip}")
|
||||
end
|
||||
n_formulaEntries = n_formulaEntries + 1
|
||||
}
|
||||
% \par\noindent\ignorespaces
|
||||
}
|
||||
% 1: equation for align environment
|
||||
|
||||
\edef\tmpFormulaName{#1}
|
||||
\par\noindent
|
||||
\begin{minipage}{\textwidth} % using a minipage to now allow line breaks within the bigformula
|
||||
\label{f:\fqname:#1}
|
||||
\par\noindent\ignorespaces
|
||||
% \textcolor{gray}{\hrule}
|
||||
% \vspace{0.5\baselineskip}
|
||||
\IfTranslationExists{\fqname:#1}{%
|
||||
\raggedright
|
||||
\GT{\fqname:#1}
|
||||
}{\detokenize{#1}}
|
||||
\IfTranslationExists{\fqname:#1_desc}{
|
||||
: {\color{fg1} \GT{\fqname:#1_desc}}
|
||||
}{}
|
||||
\hfill
|
||||
\par
|
||||
}{
|
||||
\edef\tmpContentDefs{\fqname:\tmpFormulaName_defs}
|
||||
\IfTranslationExists{\tmpContentDefs}{%
|
||||
\smartnewline
|
||||
\noindent
|
||||
\begingroup
|
||||
\color{fg1}
|
||||
\GT{\tmpContentDefs}
|
||||
% \edef\temp{\GT{#1_defs}}
|
||||
% \expandafter\StrSubstitute\expandafter{\temp}{:}{\\}
|
||||
\endgroup
|
||||
}{}
|
||||
\end{minipage}
|
||||
\separateEntries
|
||||
% \textcolor{fg3}{\hrule}
|
||||
% \vspace{0.5\baselineskip}
|
||||
\ignorespacesafterend
|
||||
}
|
||||
%
|
||||
@ -308,7 +376,8 @@
|
||||
pmf = "f:math:pt:pmf",
|
||||
cdf = "f:math:pt:cdf",
|
||||
mean = "f:math:pt:mean",
|
||||
variance = "f:math:pt:variance"
|
||||
variance = "f:math:pt:variance",
|
||||
median = "f:math:pt:median",
|
||||
}
|
||||
if cases["\luaescapestring{##1}"] \string~= nil then
|
||||
tex.sprint("\\hyperref["..cases["\luaescapestring{##1}"].."]{\\GT{##1}}")
|
||||
@ -341,6 +410,7 @@
|
||||
\edef\tmpMinipagetableWidth{#1}
|
||||
\edef\tmpMinipagetableName{#2}
|
||||
\directlua{
|
||||
table_name = "\luaescapestring{#2}"
|
||||
entries = {}
|
||||
}
|
||||
|
||||
@ -357,6 +427,8 @@
|
||||
}
|
||||
}{
|
||||
% \hfill
|
||||
% reset the fqname
|
||||
\edef\fqname{\tmpFqname}
|
||||
\begin{minipage}{\tmpMinipagetableWidth}
|
||||
\begingroup
|
||||
\setlength{\tabcolsep}{0.9em} % horizontal
|
||||
@ -365,12 +437,11 @@
|
||||
\hline
|
||||
\directlua{
|
||||
for _, k in ipairs(entries) do
|
||||
tex.print("\\GT{" .. k .. "} & \\gt{\tmpMinipagetableName:" .. k .. "}\\\\")
|
||||
tex.print("\\GT{" .. k .. "} & \\gt{"..table_name..":"..k .."}\\\\")
|
||||
end
|
||||
}
|
||||
\hline
|
||||
\end{tabularx}
|
||||
\endgroup
|
||||
\end{minipage}
|
||||
% reset the fqname
|
||||
}
|
||||
|
||||
@ -1,28 +1,67 @@
|
||||
\newcommand\smartnewline[1]{\ifhmode\\\fi} % newline only if there in horizontal mode
|
||||
\def\gooditem{\item[{$\color{neutral_red}\bullet$}]}
|
||||
\def\baditem{\item[{$\color{neutral_green}\bullet$}]}
|
||||
\def\gooditem{\item[{$\color{fg-red}\bullet$}]}
|
||||
\def\baditem{\item[{$\color{fg-green}\bullet$}]}
|
||||
|
||||
% Functions with (optional) paranthesis
|
||||
% 1: The function (like \exp, \sin etc.)
|
||||
% 2: The argument (optional)
|
||||
% If an argument is provided, it is wrapped in paranthesis.
|
||||
\newcommand\CmdWithParenthesis[2]{
|
||||
\ifstrequal{#2}{\relax}{
|
||||
#1
|
||||
}{
|
||||
#1\left(#2\right)
|
||||
}
|
||||
}
|
||||
\newcommand\CmdInParenthesis[2]{
|
||||
\ifstrequal{#2}{\relax}{
|
||||
#1
|
||||
}{
|
||||
\left(#1 #2\right)
|
||||
}
|
||||
}
|
||||
|
||||
|
||||
% COMMON SYMBOLS WITH SUPER/SUBSCRIPTS, VECTOR ARROWS ETC.
|
||||
% \def\laplace{\Delta} % Laplace operator
|
||||
\def\laplace{\bigtriangleup} % Laplace operator
|
||||
\def\Grad{\vec{\nabla}}
|
||||
\def\Div{\vec{\nabla} \cdot}
|
||||
\def\Rot{\vec{\nabla} \times}
|
||||
% symbols
|
||||
\def\Grad{\vec{\nabla}}
|
||||
\def\Div {\vec{\nabla} \cdot}
|
||||
\def\Rot {\vec{\nabla} \times}
|
||||
% symbols with parens
|
||||
\newcommand\GradS[1][\relax]{\CmdInParenthesis{\Grad}{#1}}
|
||||
\newcommand\DivS [1][\relax]{\CmdInParenthesis{\Div} {#1}}
|
||||
\newcommand\RotS [1][\relax]{\CmdInParenthesis{\Rot} {#1}}
|
||||
% text with parens
|
||||
\newcommand\GradT[1][\relax]{\CmdWithParenthesis{\text{grad}\,}{#1}}
|
||||
\newcommand\DivT[1][\relax] {\CmdWithParenthesis{\text{div}\,} {#1}}
|
||||
\newcommand\RotT[1][\relax] {\CmdWithParenthesis{\text{rot}\,} {#1}}
|
||||
\def\vecr{\vec{r}}
|
||||
\def\vecR{\vec{R}}
|
||||
\def\veck{\vec{k}}
|
||||
\def\vecx{\vec{x}}
|
||||
\def\kB{k_\text{B}} % boltzmann
|
||||
\def\NA{N_\text{A}} % avogadro
|
||||
\def\EFermi{E_\text{F}}
|
||||
\def\Evalence{E_\text{v}}
|
||||
\def\Econd{E_\text{c}}
|
||||
\def\Egap{E_\text{gap}}
|
||||
\def\masse{m_\textrm{e}}
|
||||
\def\Four{\mathcal{F}} % Fourier transform
|
||||
\def\kB{k_\text{B}} % boltzmann
|
||||
\def\NA{N_\text{A}} % avogadro
|
||||
\def\EFermi{E_\text{F}} % fermi energy
|
||||
\def\Efermi{E_\text{F}} % fermi energy
|
||||
\def\Evalence{E_\text{v}} % val vand energy
|
||||
\def\Econd{E_\text{c}} % cond. band nergy
|
||||
\def\Egap{E_\text{gap}} % band gap energy
|
||||
\def\Evac{E_\text{vac}} % vacuum energy
|
||||
\def\masse{m_\text{e}} % electron mass
|
||||
\def\Four{\mathcal{F}} % Fourier transform
|
||||
\def\Lebesgue{\mathcal{L}} % Lebesgue
|
||||
\def\O{\mathcal{O}}
|
||||
\def\PhiB{\Phi_\text{B}}
|
||||
\def\PhiE{\Phi_\text{E}}
|
||||
\def\O{\mathcal{O}} % order
|
||||
\def\PhiB{\Phi_\text{B}} % mag. flux
|
||||
\def\PhiE{\Phi_\text{E}} % electric flux
|
||||
\def\nreal{n^{\prime}} % refraction real part
|
||||
\def\ncomplex{n^{\prime\prime}} % refraction index complex part
|
||||
\def\I{i} % complex unit
|
||||
\def\crit{\text{crit}} % crit (for subscripts)
|
||||
\def\muecp{\overline{\mu}} % electrochemical potential
|
||||
\def\pH{\text{pH}} % pH
|
||||
\def\rfactor{\text{rf}} % rf roughness_factor
|
||||
|
||||
|
||||
% SYMBOLS
|
||||
@ -87,8 +126,6 @@
|
||||
\def\txx{\text{x}}
|
||||
\def\txy{\text{y}}
|
||||
\def\txz{\text{z}}
|
||||
% complex, may be changed later to idot or upright...
|
||||
\def\I{i}
|
||||
|
||||
% SPACES
|
||||
\def\sdots{\,\dots\,}
|
||||
@ -104,16 +141,18 @@
|
||||
\newcommand{\explOverEq}[2][=]{%
|
||||
\overset{\substack{\mathrlap{\text{\hspace{-1em}#2}}\\\downarrow}}{#1}}
|
||||
\newcommand{\eqnote}[1]{
|
||||
\text{\color{dark2}#1}
|
||||
\text{\color{fg2}#1}
|
||||
}
|
||||
|
||||
|
||||
% DELIMITERS
|
||||
\DeclarePairedDelimiter{\abs}{\lvert}{\rvert}
|
||||
\DeclarePairedDelimiter{\floor}{\lfloor}{\rfloor}
|
||||
\DeclarePairedDelimiter{\ceil}{\lceil}{\rceil}
|
||||
% not using DeclarePairedDelmiter to always get scaling
|
||||
\newcommand{\abs}[1]{\left\lvert #1 \right\rvert}
|
||||
\newcommand{\floor}[1]{\left\lfloor#1\right\rfloor}
|
||||
\newcommand{\ceil}[1]{\left\lceil#1\right\rceil}
|
||||
|
||||
% OPERATORS
|
||||
% * places subset under the word instead of next to it
|
||||
\DeclareMathOperator{\e}{e}
|
||||
\def\T{\text{T}} % transposed
|
||||
\DeclareMathOperator{\sgn}{sgn}
|
||||
@ -122,6 +161,12 @@
|
||||
\DeclareMathOperator{\erf}{erf}
|
||||
\DeclareMathOperator{\erfc}{erfc}
|
||||
\DeclareMathOperator{\cov}{cov}
|
||||
|
||||
\DeclareMathOperator*{\argmin}{arg\,min}
|
||||
\DeclareMathOperator*{\argmax}{arg\,max}
|
||||
% \DeclareMathOperator{\div}{div}
|
||||
% \DeclareMathOperator{\grad}{grad}
|
||||
% \DeclareMathOperator{\rot}{rot}
|
||||
% \DeclareMathOperator{\arcsin}{arcsin}
|
||||
% \DeclareMathOperator{\arccos}{arccos}
|
||||
% \DeclareMathOperator{\arctan}{arctan}
|
||||
@ -135,22 +180,22 @@
|
||||
\renewcommand*\d{\mathop{}\!\mathrm{d}}
|
||||
% times 10^{x}
|
||||
\newcommand\xE[1]{\cdot 10^{#1}}
|
||||
% functions with paranthesis
|
||||
\newcommand\CmdWithParenthesis[2]{
|
||||
#1\left(#2\right)
|
||||
}
|
||||
\newcommand\Exp[1]{\CmdWithParenthesis{\exp}{#1}}
|
||||
\newcommand\Sin[1]{\CmdWithParenthesis{\sin}{#1}}
|
||||
\newcommand\Cos[1]{\CmdWithParenthesis{\cos}{#1}}
|
||||
\newcommand\Ln[1]{\CmdWithParenthesis{\ln}{#1}}
|
||||
\newcommand\Log[1]{\CmdWithParenthesis{\log}{#1}}
|
||||
\newcommand\Order[1]{\CmdWithParenthesis{\mathcal{O}}{#1}}
|
||||
|
||||
% VECTOR AND MATRIX
|
||||
% VECTOR, MATRIX and TENSOR
|
||||
% use vecA to force an arrow
|
||||
\NewCommandCopy{\vecA}{\vec}
|
||||
% extra {} assure they can b directly used after _
|
||||
%% arrow/underline
|
||||
\newcommand\mat[1]{{\ensuremath{\underline{#1}}}}
|
||||
\renewcommand\vec[1]{{\ensuremath{\vecA{#1}}}}
|
||||
\newcommand\ten[1]{{\ensuremath{[#1]}}}
|
||||
\newcommand\complex[1]{{\ensuremath{\tilde{#1}}}}
|
||||
%% bold
|
||||
% \newcommand\mat[1]{{\ensuremath{\bm{#1}}}}
|
||||
% \renewcommand\vec[1]{{\ensuremath{\bm{#1}}}}
|
||||
|
||||
@ -76,7 +76,7 @@
|
||||
}
|
||||
\end{ContentBoxWithExplanation}
|
||||
\endgroup
|
||||
\textcolor{dark3}{\hrule}
|
||||
\textcolor{fg3}{\hrule}
|
||||
\vspace{0.5\baselineskip}
|
||||
\ignorespacesafterend
|
||||
}
|
||||
@ -93,22 +93,22 @@
|
||||
% PERIODIC TABLE
|
||||
\directlua{
|
||||
category2color = {
|
||||
metal = "neutral_blue",
|
||||
metalloid = "bright_orange",
|
||||
transitionmetal = "bright_blue",
|
||||
lanthanoide = "neutral_orange",
|
||||
alkalimetal = "bright_red",
|
||||
alkalineearthmetal = "bright_purple",
|
||||
nonmetal = "bright_aqua",
|
||||
halogen = "bright_yellow",
|
||||
noblegas = "neutral_purple"
|
||||
metal = "bg-blue!50!bg0",
|
||||
metalloid = "fg-orange!50!bg0",
|
||||
transitionmetal = "fg-blue!50!bg0",
|
||||
lanthanoide = "bg-orange!50!bg0",
|
||||
alkalimetal = "fg-red!50!bg0",
|
||||
alkalineearthmetal = "fg-purple!50!bg0",
|
||||
nonmetal = "fg-aqua!50!bg0",
|
||||
halogen = "fg-yellow!50!bg0",
|
||||
noblegas = "bg-purple!50!bg0"
|
||||
}
|
||||
}
|
||||
\directlua{
|
||||
function getColor(cat)
|
||||
local color = category2color[cat]
|
||||
if color == nil then
|
||||
return "light3"
|
||||
return "bg3"
|
||||
else
|
||||
return color
|
||||
end
|
||||
@ -138,7 +138,7 @@
|
||||
end
|
||||
end
|
||||
}
|
||||
\draw[ultra thick,faded_purple] (4,-6) -- (4,-11);
|
||||
\draw[ultra thick,fg-purple] (4,-6) -- (4,-11);
|
||||
% color legend for categories
|
||||
\directlua{
|
||||
local x0 = 4
|
||||
|
||||
105
src/util/tikz_macros.tex
Normal file
105
src/util/tikz_macros.tex
Normal file
@ -0,0 +1,105 @@
|
||||
|
||||
\tikzset{
|
||||
% bands
|
||||
sc band con/.style={ draw=fg0, thick},
|
||||
sc band val/.style={ draw=fg0, thick},
|
||||
sc band vac/.style={ draw=fg1, thick},
|
||||
sc band/.style={ draw=fg0, thick},
|
||||
sc fermi level/.style={draw=fg-aqua,dashed,thick},
|
||||
% electron filled
|
||||
sc occupied/.style={
|
||||
pattern=north east lines,
|
||||
pattern color=fg-aqua,
|
||||
draw=none
|
||||
},
|
||||
% materials
|
||||
sc p type/.style={ draw=none,fill=bg-yellow!20},
|
||||
sc n type/.style={ draw=none,fill=bg-blue!20},
|
||||
sc metal/.style={ draw=none,fill=bg-purple!20},
|
||||
sc oxide/.style={ draw=none,fill=bg-green!20},
|
||||
sc separate/.style={ draw=fg0,dotted},
|
||||
}
|
||||
|
||||
\newcommand\drawDArrow[4]{
|
||||
\draw[<->] (#1,#2) -- (#1,#3) node[midway,right] () {#4};
|
||||
}
|
||||
% Band bending down at L-R interface: BendH must be negative
|
||||
% need two functions for different out= angles, or use if else on the sign of BendH
|
||||
\newcommand\leftBandAuto[2]{
|
||||
\directlua{
|
||||
if \tkLBendH == 0 then
|
||||
tex.print([[(\tkLx,#2) \ifblank{#1}{}{node[anchor=east] \detokenize{{#1}}} -- (\tkLW,#2) ]])
|
||||
else
|
||||
if \tkLBendH > 0 then
|
||||
angle = 180+45
|
||||
else
|
||||
angle = 180-45
|
||||
end
|
||||
tex.sprint([[(\tkLx,#2) \ifblank{#1}{}{node[anchor=east] \detokenize{{#1}}}
|
||||
-- (\tkLW-\tkLBendW,#2) to[out=0,in=]], angle, [[](\tkLW,#2+\tkLBendH)]])
|
||||
end
|
||||
}
|
||||
% % \ifthenelse{\equal{\tkLBendH}{0}}%
|
||||
% % {%
|
||||
% \ifthenelse{\tkLBendH > 0}%
|
||||
% {\pgfmathsetmacro{\angle}{-45}}%
|
||||
% {\pgfmathsetmacro{\angle}{45}}%
|
||||
% % }
|
||||
}
|
||||
\newcommand\rightBandAuto[2]{
|
||||
\directlua{
|
||||
if \tkRBendH == 0 then
|
||||
%-- tex.print([[\rightBand{#1}{#2}]])
|
||||
tex.print([[(\tkRx,#2) -- (\tkW,#2)]]) %-- \ifblank{#1}{}{node[anchor=west] \{#1\}}]])
|
||||
else
|
||||
if \tkRBendH > 0 then
|
||||
angle = -45
|
||||
else
|
||||
angle = 45
|
||||
end
|
||||
tex.sprint([[(\tkRx,#2+\tkRBendH) to[out=]], angle, [[,in=180] (\tkRx+\tkRBendW,#2) -- (\tkW,#2) ]])
|
||||
%-- \ifblank{#1}{}{node[anchor=west] \{#1\}} ]])
|
||||
end
|
||||
if "\luaescapestring{#1}" \string~= "" then
|
||||
tex.print([[node[anchor=west] \detokenize{{#1}} ]])
|
||||
end
|
||||
}
|
||||
% \ifthenelse{\equal{\tkRBendH}{0}}%
|
||||
% {\rightBand{#1}{#2}}
|
||||
% {%
|
||||
% \ifthenelse{\tkRBendH > 0}%
|
||||
% {\pgfmathsetmacro{\angle}{-45}}%
|
||||
% {\pgfmathsetmacro{\angle}{45}}%
|
||||
% (\tkRx,#2+\tkRBendH) to[out=45,in=180] (\tkRx+\tkRBendW,#2) -- (\tkW,#2)
|
||||
% \ifblank{#1}{}{node[anchor=west]{#1}}
|
||||
% }
|
||||
}
|
||||
\newcommand\leftBandDown[2]{
|
||||
(\tkRx,#2+\tkRBendH) to[out=45,in=180] (\tkRx+\tkRBendW,#2) -- (\tkW,#2)
|
||||
\ifblank{#1}{}{node[anchor=west]{#1}}
|
||||
}
|
||||
\newcommand\rightBandDown[2]{
|
||||
(\tkRx,#2+\tkRBendH) to[out=45,in=180] (\tkRx+\tkRBendW,#2) -- (\tkW,#2)
|
||||
\ifblank{#1}{}{node[anchor=west]{#1}}
|
||||
}
|
||||
% Band bending down at L-R interface: BendH must be positive
|
||||
\newcommand\leftBandUp[2]{
|
||||
(\tkLx,#2) \ifblank{#1}{}{node[anchor=east]{#1}}
|
||||
-- (\tkLW-\tkLBendW,#2) to[out=0,in=180+45] (\tkLW,#2+\tkLBendH)
|
||||
}
|
||||
\newcommand\rightBandUp[2]{
|
||||
(\tkRx,#2+\tkRBendH) to[out=-45,in=180] (\tkRx+\tkRBendW,#2) -- (\tkW,#2)
|
||||
\ifblank{#1}{}{node[anchor=west]{#1}}
|
||||
}
|
||||
% Straight band
|
||||
\newcommand\leftBand[2]{
|
||||
(\tkLx,#2) \ifblank{#1}{}{node[anchor=east]{#1}} -- (\tkLW,#2)
|
||||
}
|
||||
\newcommand\rightBand[2]{
|
||||
(\tkRx,#2) -- (\tkW,#2) \ifblank{#1}{}{node[anchor=west]{#1}}
|
||||
}
|
||||
|
||||
\newcommand\drawAxes{
|
||||
\draw[->] (0,0) -- (\tkW+0.2,0) node[anchor=north] {$x$};
|
||||
\draw[->] (0,0) -- (0,\tkH+0.2) node[anchor=east] {$E$};
|
||||
}
|
||||
@ -26,11 +26,18 @@
|
||||
% \expandafter\IfTranslationExists\expandafter{\fqname:#1}
|
||||
}
|
||||
|
||||
\newcommand{\gt}[1]{%
|
||||
\iftranslation{#1}{%
|
||||
\newrobustcmd{\robustGt}[1]{%
|
||||
\IfTranslationExists{\fqname:#1}{%
|
||||
\expandafter\GetTranslation\expandafter{\fqname:#1}%
|
||||
}{%
|
||||
\detokenize{\fqname}:\detokenize{#1}%
|
||||
\printFqName:\detokenize{#1}%
|
||||
}%
|
||||
}
|
||||
\newcommand{\gt}[1]{%
|
||||
\IfTranslationExists{\fqname:#1}{%
|
||||
\expandafter\GetTranslation\expandafter{\fqname:#1}%
|
||||
}{%
|
||||
\printFqName:\detokenize{#1}%
|
||||
}%
|
||||
}
|
||||
\newrobustcmd{\GT}[1]{%\expandafter\GetTranslation\expandafter{#1}}
|
||||
@ -40,6 +47,9 @@
|
||||
\detokenize{#1}%
|
||||
}%
|
||||
}
|
||||
% text variants for use in math mode
|
||||
\newcommand{\tgt}[1]{\text{\gt{#1}}}
|
||||
\newcommand{\tGT}[1]{\text{\GT{#1}}}
|
||||
|
||||
% Define a translation and also make the fallback if it is the english translation
|
||||
% 1: lang, 2: key, 3: translation
|
||||
|
||||
@ -25,6 +25,16 @@
|
||||
\Eng[diamond]{Diamond}
|
||||
\Ger[diamond]{Diamant}
|
||||
|
||||
\Eng[metal]{Metal}
|
||||
\Ger[metal]{Metall}
|
||||
|
||||
\Eng[semiconductor]{Semiconductor}
|
||||
\Ger[semiconductor]{Halbleiter}
|
||||
|
||||
|
||||
\Eng[creation_annihilation_ops]{Creation / Annihilation operators}
|
||||
\Ger[creation_annihilation_ops]{Erzeugungs / Vernichtungs-Operatoren}
|
||||
|
||||
% FORMATING
|
||||
\Eng[list_of_quantitites]{List of quantitites}
|
||||
\Ger[list_of_quantitites]{Liste von Größen}
|
||||
@ -32,6 +42,9 @@
|
||||
\Eng[other]{Others}
|
||||
\Ger[other]{Sonstige}
|
||||
|
||||
\Eng[sometimes]{sometimes}
|
||||
\Ger[sometimes]{manchmal}
|
||||
|
||||
\Eng[see_also]{See also}
|
||||
\Ger[see_also]{Siehe auch}
|
||||
|
||||
|
||||
Loading…
x
Reference in New Issue
Block a user