MatthiasQuintern/formelsammlung
1
0
Fork 0
Code Issues Pull Requests Packages Projects Releases 2 Wiki Activity

fixes

Browse Source
This commit is contained in:
matthias@quintern.xyz 2024-11-30 16:50:47 +01:00
parent 02c1d40bc9
commit 2c2da27752
15 changed files with 361 additions and 165 deletions
Show Stats Download Patch File Download Diff File Expand all files Collapse all files

1
src/atom.tex
View File

@ -178,5 +178,4 @@
\ger{Effekte im Magnetfeld}
]{mag_effects}
\TODO{all}
\\\TODO{Hunds rules}

68
src/condensed_matter.tex
View File

@ -85,6 +85,8 @@
\end{tabularx}
\end{adjustbox}
\end{table}
\TODO{FCC, BCC, diamond/Zincblende wurtzize cell/lattice vectors}
\TODO{primitive unit cell: contains one lattice point}\\
family of plane that are equivalent due to crystal symmetry
\begin{formula}{miller}
@ -254,6 +256,26 @@ family of plane that are equivalent due to crystal symmetry
\TODO{TODO}
\Section[
\eng{Semiconductors}
\ger{Halbleiter}
]{semic}
\begin{formula}{charge_density_eq}
\desc{Equilibrium charge densitites}{}{}
\desc[german]{Ladungsträgerdichte im Equilibrium}{}{}
\eq{
n_0 &\approx N_\text{c}(T) e^{-\frac{E_\text{c} - \EFermi}{\kB T}} \\
p_0 &\approx N_\text{v}(T) e^{-\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)} e^{-\frac{E_\text{gap}}{2\kB T}}
}
\end{formula}
\Section[
\eng{Measurement techniques}
\ger{Messtechniken}
@ -408,49 +430,3 @@ family of plane that are equivalent due to crystal symmetry
\includegraphics[width=\textwidth]{img/cm_mbe_english.pdf}
\end{minipage}
\Section[
\eng{Superconductivity}
\ger{Supraleitung}
]{sc}
\begin{ttext}
\eng{
Materials for which the electric resistance jumps to 0 under a critical temperature.
\\\textbf{Type I}: Has a single critical magnetic field at which the superconuctor becomes a normal conductor.
\\\textbf{Type II}: Has two critical
}
\ger{Materialien, bei denen der elektrische Widerstand beim unterschreiten einer kritischen Temperatur auf 0 springt.}
\end{ttext}
\begin{formula}{meissner_effect}
\desc{Meißner-Ochsenfeld effect}{Perfect diamagnetism}{}
\desc[german]{Meißner-Ochsenfeld Effekt}{Perfekter Diamagnetismus}{}
\ttxt{
\eng{Blabla }
\ger{Blubb blubb }
}
\end{formula}
\Subsection[
\eng{London equation}
\ger{London-Gleichungen}
]{london}
\begin{formula}{first}
% \vec{j} = \frac{nq\hbar}{m}\Grad S - \frac{nq^2}{m}\vec{A}
\desc{First London Equation}{}{$\vec{j}$ current density, $n$, $m$, $q$ density, mass and charge of superconduticng particles}
\desc[german]{Erste London-Gleichung}{}{$\vec{j}$ Stromdichte, $n$, $m$, $q$ Dichte, Masse und Ladung der supraleitenden Teilchen}
\eq{
\partical_t \vec{j} = \frac{nq^2}{m}\vec{E}
}
\end{formula}
\begin{formula}{second}
\desc{Second London Equation}{}{$\vec{j}$ current density, $n$, $m$, $q$ density, mass and charge of superconduticng particles}
\desc[german]{Zweite London-Gleichung}{}{$\vec{j}$ Stromdichte, $n$, $m$, $q$ Dichte, Masse und Ladung der supraleitenden Teilchen}
\eq{
\Rot \vec{j} = -\frac{nq^2}{m} \vec{B}
}
\end{formula}
\begin{formula}{penetration_depth}
\desc{London penetration depth}{}{}
\desc[german]{London Eindringtiefe}{}{}
\eq{\lambda_\textrm{L} = \sqrt{\frac{m}{\mu_0 nq^2}}}
\end{formula}

60
src/electrodynamics.tex
View File

@ -42,7 +42,7 @@
\Subsection[
\eng{Electric field}
\ger{Elektrisches Feld}
]{mag}
]{el}
\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}
@ -57,11 +57,10 @@
\Eng[magnetic_flux]{Magnetix flux density}
\Ger[magnetic_flux]{Magnetische Flussdichte}
% \begin{quantity}{mag_flux}{\Phi}{\Wb}{\kg\m^2\per\s^2\A^1}{scalar}
% \sign{}
% \desc{Magnetic flux density}{}
% \desc[german]{Magnetische Feldstärke}{}
% \end{quantity}
\begin{quantity}{mag_flux}{\Phi}{\weber=\volt\per\s=\kg\m^2\per\s^2\A}{scalar}
\desc{Magnetic flux}{}
\desc[german]{Magnetischer Fluss}{}
\end{quantity}
\begin{formula}{magnetic_flux}
\desc{Magnetic flux}{}{}
@ -75,11 +74,6 @@
\eq{\PhiB = \iint_S \vec{B}\cdot\d\vec{S} = 0}
\end{formula}
\begin{formula}{name}
\desc{}{}{}
\desc[german]{}{}{}
\eq{}
\end{formula}
\begin{formula}{magnetization}
\desc{Magnetization}{}{$m$ mag. moment, $V$ volume}
\desc[german]{Magnetisierung}{}{$m$ mag. Moment, $V$ Volumen}
@ -109,7 +103,7 @@
\Subsection[
\eng{Induction}
\ger{Unduktion}
\ger{Induktion}
]{induction}
\begin{formula}{farady_law}
\desc{Faraday's law of induction}{}{}
@ -117,6 +111,19 @@
\eq{U_\text{ind} = -\odv{}{t} \PhiB = - \odv{}{t} \iint_A\vec{B} \cdot \d\vec{A}}
\end{formula}
\begin{formula}{lenz}
\desc{Lenz's law}{}{}
\desc[german]{Lenzsche Regel}{}{}
\ttxt{
\eng{
Change of magnetic flux through a conductor induces a current that counters that change of magnetic flux.
}
\ger{
Die Änderung des magnetischen Flußes durch einen Leiter induziert einen Strom der der Änderung entgegenwirkt.
}
}
\end{formula}
\Section[
\eng{Hall-Effect}
\ger{Hall-Effekt}
@ -178,8 +185,8 @@
\end{formula}
\begin{formula}{resistivity}
\desc{Resistivity}{}{$\nu \in \mathbb{Z}$}
\desc[german]{Spezifischer Hallwiderstand}{}{$\nu \in \mathbb{Z}$}
\desc{Resistivity}{}{$\nu \in \mathbb{Z}$ filing factor}
\desc[german]{Spezifischer Hallwiderstand}{}{$\nu \in \mathbb{Z}$ Füllfaktor}
\eq{\rho_{xy} = \frac{2\pi\hbar}{e^2} \frac{1}{\nu}}
\end{formula}
@ -189,6 +196,31 @@
% \fig{img/qhe-klitzing.jpeg}
% \end{formula}
\begin{formula}{fqhe}
\desc{Fractional quantum hall effect}{}{$\nu$ fraction of two numbers without shared divisors}
\desc[german]{Fraktionaler Quantum-Hall-Effekt}{}{$\nu$ Bruch aus Zahlen ohne gemeinsamen Teiler}
\eq{\nu = \frac{1}{3},\frac{2}{5},\frac{3}{7},\frac{2}{3}...}
\end{formula}
\begin{ttext}
\eng{
\begin{itemize}
\item \textbf{Integer} (QHE): filling factor $\nu$ is an integer
\item \textbf{Fractional} (FQHE): filling factor $\nu$ is a fraction
\item \textbf{Spin} (QSHE): spin currents instead of charge currents
\item \textbf{Anomalous} (QAHE): symmetry breaking by internal effects instead of external magnetic fields
\end{itemize}
}
\ger{
\begin{itemize}
\item \textbf{Integer} (QHE): Füllfaktor $\nu$ ist ganzzahlig
\item \textbf{Fractional} (FQHE): Füllfaktor $\nu$ ist ein Bruch
\item \textbf{Spin} (QSHE): Spin Ströme anstatt Ladungsströme
\item \textbf{Anomalous} (QAHE): Symmetriebruch durch interne Effekte anstatt druch ein externes Magnetfeld
\end{itemize}
}
\end{ttext}
\TODO{sort}
\begin{formula}{impedance_c}

93
src/main.tex Executable file → Normal file
View File

@ -36,6 +36,11 @@
\usepackage{tikz} % drawings
\usetikzlibrary{decorations.pathmorphing}
\usetikzlibrary{calc}
% speed up compilation by externalizing figures
% \usetikzlibrary{external}
% \tikzexternalize[prefix=tikz_figures]
% \tikzexternalize
\usepackage{circuitikz}
% SCIENCE PACKAGES
@ -114,7 +119,13 @@
% Make the translation of #1 a reference to a equation
% 1: key
\newcommand{\fqEqRef}[1]{
\hyperref[eq:#1]{\GT{#1}}
\edef\fqeqrefname{\GT{#1}}
\hyperref[eq:#1]{\fqeqrefname}
}
\newcommand{\qtyRef}[1]{
% using temp edef so that underscores in undefined trasnlation keys are printed as characters
\edef\qtyrefname{\GT{qty:#1}}
\hyperref[qty:#1]{\qtyrefname}
}
% Make the translation of #1 a reference to a section
% 1: key
@ -136,6 +147,7 @@
\input{util/macros.tex}
\input{util/environments.tex}
% \includeonly{computational}
\begin{document}
\maketitle
@ -145,29 +157,80 @@
\input{util/translations.tex}
\input{maths/linalg.tex}
\input{maths/geometry.tex}
\input{maths/analysis.tex}
\input{maths/probability_theory.tex}
% \include{maths/linalg}
% \include{maths/geometry}
% \include{maths/analysis}
% \include{maths/probability_theory}
\input{mechanics.tex}
\include{mechanics}
\input{statistical_mechanics.tex}
\include{statistical_mechanics}
\input{electrodynamics.tex}
\include{electrodynamics}
\input{quantum_mechanics.tex}
\input{atom.tex}
\include{quantum_mechanics}
\include{atom}
\input{condensed_matter.tex}
\include{condensed_matter}
\include{low_temp}
\input{topo.tex}
\include{topo}
\input{quantum_computing.tex}
\include{quantum_computing}
% \input{many-body-simulations.tex}
\include{computational}
%\newpage
\include{quantities}
\newpage
% \DT[english]{ttest}{TESTT EN}
% \DT[german]{ttest}{TESTT DE}
\addtranslation{english}{ttest}{JA MOIN}
\noindent
GT: ttest = \GT{ttest}\\
GetTranslation: ttest = \GetTranslation{ttest}\\
Is english? = \IfTranslation{english}{ttest}{yes}{no} \\
Is german? = \IfTranslation{german}{ttest}{yes}{no} \\
Is defined = \IfTranslationExists{ttest}{yes}{no} \\
\def\ttest{NAME}
% \addtranslation{english}{\ttest:name}{With variable}
% \addtranslation{german}{\ttest:name}{Mit Variable}
% \addtranslation{english}{NAME:name}{Without variable}
% \addtranslation{german}{NAME:name}{Without Variable}
\DT[\ttest:name]{english}{DT With variable}
\DT[\ttest:name]{german}{DT Mit Variable}
\noindent
GT: {\textbackslash}ttest:name = \GT{\ttest:name}\\
GetTranslation: {\textbackslash}ttest:name = \GetTranslation{\ttest:name}\\
Is english? = \IfTranslation{english}{\ttest:name}{yes}{no} \\
Is german? = \IfTranslation{german}{\ttest:name}{yes}{no} \\
Is defined? = \IfTranslationExists{\ttest:name}{yes}{no} \\
Is defined? = \expandafter\IfTranslationExists\expandafter{\ttest:name}{yes}{no}
% \DT[qty:test]{english}{HAHA}
{blablabla \label{test}}
\hyperref[test]{TEST reference}
\qtyRef{test}
\DT[qty:test]{english}{HAHA}
\qtyRef{mass}
\GT{qty:#1}
\GT{\qtyname}
\newpage
\Eng[appendix]{Appendix}
\Ger[appendix]{Anhang}
\part*{\GT{appendix}}
% \listofmyenv
\listofquantities
\listoffigures
\listoftables
% \bibliographystyle{plain}
% \bibliography{ref}
\end{document}

10
src/many-body-simulations.tex
View File

@ -1,10 +0,0 @@
\Part[
\eng{Many-body simulations}
\ger{Vielteilchen Simulationen}
]{mbsim}
\Section[
\eng{Importance sampling}
\ger{Importance sampling / Stichprobenentnahme nach Wichtigkeit}
]{importance_sampling}

4
src/maths/analysis.tex
View File

@ -125,8 +125,8 @@
\end{formula}
\begin{formula}{error-function}
\desc{Error function}{\erf: \C \to \C}{}
\desc[german]{Fehlerfunktion}{Error function: \erf: \C \to \C}{}
\desc{Error function}{$\erf: \C \to \C$ and complementary error function $\erfc$}{}
\desc[german]{Fehlerfunktion}{$\erf: \C \to \C$ und komplementäre Fehlerfunktion $\erfc$}{}
\eq{
\erf(x) &= \frac{2}{\sqrt{\pi}} \int_0^x e^{-t^2} \d t \\
\erfc(x) &= 1 - \erf(x)\\

12
src/mechanics.tex
View File

@ -3,6 +3,18 @@
\ger{Mechanik}
]{mech}
\Section[
\eng{Misc}
\ger{Verschiedenes}
]{misc}
\begin{formula}{hook}
\desc{Hooke's law}{}{$F$ \qtyRef{force}, $D$ \qtyRef{spring_constant}, $\Delta l$ spring length}
\desc[german]{Hookesches Gesetz}{}{$F$ \qtyRef{force}, $D$ \qtyRef{spring_constant}, $\Delta l$ Federlänge}
\eq{
F = D\Delta l
}
\end{formula}
\def\lagrange{\mathcal{L}}
\Section[
\eng{Lagrange formalism}

41
src/quantum_computing.tex
View File

@ -94,9 +94,9 @@
\desc[german]{SQUID}{Superconducting quantum interference device, besteht aus parralelen \hyperref{sec:qc:scq:josephson_junction}{Josephson Junctions} und kann zur Messung extrem schwacher Magnetfelder genutzt werden}{}
\content{
\centering
\begin{circuitikz}
\begin{tikzpicture}
\draw (0, 0) \squidloop{loop}{};
\end{circuitikz}
\end{tikzpicture}
}
\end{formula}
\begin{formula}{hamiltonian}
@ -109,7 +109,7 @@
\eng{Josephson Qubit??}
\ger{TODO}
]{josephson_qubit}
\begin{circuitikz}
\begin{tikzpicture}
\draw (0,0) to[capacitor] (0,2);
\draw (0,0) to (2,0);
\draw (0,2) to (2,2);
@ -117,10 +117,10 @@
\draw[->] (3,1) -- (4,1);
\draw (5,0) to[josephsoncap=$C_\text{J}$] (5,2);
\end{circuitikz}
\end{tikzpicture}
\TODO{Include schaltplan}
\begin{circuitikz}
\begin{tikzpicture}
\draw (0,0) to[sV=$V_\text{g}$] (0,2);
\draw (0,2) to[capacitor=$C_\text{g}$] (2,2);
\draw (2,2) to (4,2);
@ -128,7 +128,7 @@
\draw (4,0) to[capacitor=$C_C$] (4,2);
\draw (0,0) to (2,0);
\draw (2,0) to (4,0);
\end{circuitikz}
\end{tikzpicture}
\begin{formula}{charging_energy}
\desc{Charging energy / electrostatic energy}{}{}
@ -219,13 +219,13 @@
}{}
\content{
\centering
\begin{circuitikz}
\begin{tikzpicture}
\draw (0,0) to[sV=$V_\text{g}$] (0,2);
% \draw (0,0) to (2,0);
\draw (0,2) to[capacitor=$C_\text{g}$] (2,2);
\draw (2,0) to[josephsoncap=$C_\text{J}$] (2,2);
\draw (0,0) to (2,0);
\end{circuitikz}
\end{tikzpicture}
}
\end{formula}
@ -258,12 +258,12 @@
}{}
\content{
\centering
\begin{circuitikz}
\begin{tikzpicture}
% \draw (0,0) to[sV=$V_\text{g}$] ++(0,3)
% to[capacitor=$C_\text{g}$] ++(2,0)
\draw (0,0) to ++(2,0) to ++(0,-0.5) to[josephsoncap=$C_\text{J}$] ++(-0,-2) to ++(0,-0.5) to ++(-2,0)
to[capacitor=$C_C$] ++(0,3);
\end{circuitikz}
\end{tikzpicture}
}
\end{formula}
@ -282,14 +282,13 @@
\desc[german]{}{Durch Nutzung eines \fqSecRef{qc:scq:elements:squid} anstatt eines \fqSecRef{qc:scq:elements:josephson_junction}s, ist die Frequenz des Qubits durch ein externes Magnetfeld einstellbar}{}
\content{
\centering
\begin{circuitikz}
\begin{tikzpicture}
% \draw (0,0) to[sV=$V_\text{g}$] ++(0,3)
% to[capacitor=$C_\text{g}$] ++(2,0)
\draw (0,0) to ++(-2,0)
to ++(3,0) to ++(0,-0.5) \squidloop{loop}{SQUID} to ++(0,-0.5) to ++(-3,0)
to[capacitor=$C_C$] ++(0,3);
\end{circuitikz}
\end{tikzpicture}
}
\end{formula}
@ -321,7 +320,7 @@
\desc[german]{Phase Qubit}{}{}
\content{
\centering
\begin{circuitikz}
\begin{tikzpicture}
% \draw (0,0) to[sV=$V_\text{g}$] ++(0,3)
% to ++(2,0) coordinate(top1)
% to ++(2,0) coordinate(top2)
@ -335,7 +334,7 @@
\draw(0,0) to ++(2,0) to[josephsoncap=$C_\text{J}$] ++(0,-2) to ++(-2,0);
\draw (2,0) to ++(2,0) to[cute inductor=$E_L$] ++(0,-2) to ++(-2,0);
\node at (3,-1.5) {$\Phi_\text{ext}$};
\end{circuitikz}
\end{tikzpicture}
\\\TODO{Ist beim Fluxonium noch die Voltage source dran?}
}
\end{formula}
@ -361,15 +360,15 @@
\desc[german]{Flux Qubit / Persistent current qubit}{}{}
\content{
\centering
\begin{circuitikz}
\begin{tikzpicture}
\draw (0,0) to[josephsoncap=$\alpha E_\text{J}$, scale=0.8, transform shape] (0,-3);
\draw (0,0) to ++(3,0)
to[josephsoncap=$E_\text{J}$] ++(0,-1.5)
to[josephsoncap=$E_\text{J}$] ++(0,-1.5)
to ++(-3,0);
\node at (1.5,-1.5) {$\Phi_\text{ext}$};
\end{circuitikz}
% \begin{circuitikz}
\end{tikzpicture}
% \begin{tikzpicture}
% \draw (0,0) to[sV=$V_\text{g}$] ++(0,3)
% to ++(2,0) coordinate(top1)
% to ++(2,0) coordinate(top2)
@ -385,7 +384,7 @@
% to[josephsoncap=$E_\text{J}$] ++(0,-1.5)
% to[josephsoncap=$E_\text{J}$] (bot3);
% \node at (5,0.5) {$\Phi_\text{ext}$};
% \end{circuitikz}
% \end{tikzpicture}
}
\end{formula}
@ -406,14 +405,14 @@
}{}
\content{
\centering
\begin{circuitikz}
\begin{tikzpicture}
% \draw (0,0) to[sV=$V_\text{g}$] ++(0,3)
% to ++(2,0) coordinate(top1);
\draw[color=gray] (0,0) to ++(-2,0) to[capacitor=$C_C$] ++(0,-3) to ++(2,0);
\draw (0,0) to[josephsoncap=$C_\text{J}$] ++(-0,-3);
\draw (0,0) to ++(2,0) to[cute inductor=$E_L$] ++(0,-3) to ++(-2,0);
\node at (1,-0.5) {$\Phi_\text{ext}$};
\end{circuitikz}
\end{tikzpicture}
\\\TODO{Ist beim Fluxonium noch die Voltage source dran?}
}
\end{formula}

79
src/quantum_mechanics.tex
View File

@ -211,6 +211,14 @@
\eq{\dot{\rho} = \underbrace{-\frac{i}{\hbar} [\hat{H}, \rho]}_\text{reversible} + \underbrace{\sum_{n.m} h_{nm} \left(\hat{A}_n\rho \hat{A}_{m^\dagger} - \frac{1}{2}\left\{\hat{A}_m^\dagger \hat{A}_n,\rho \right\}\right)}_\text{irreversible}}
\end{formula}
\begin{formula}{hellmann_feynmann}
\desc{Hellmann-Feynman-Theorem}{Derivative of the energy to a parameter}{}
\desc[german]{Hellmann-Feynman-Theorem}{Abletiung der Energie nach einem Parameter}{}
\eq{
\odv{E_\lambda}{\lambda} = \int \d^3r \psi^*_\lambda \odv{\hat{H}_\lambda}{\lambda} \psi_\lambda = \Braket{\psi(\lambda)|\odv{\hat{H}_{\lambda}}{\lambda}|\psi(\lambda)}
}
\end{formula}
\TODO{unitary transformation of time dependent H}
@ -250,15 +258,15 @@
]{ehrenfest_theorem}
\GT{see_also} \ref{sec:qm:basics:schroedinger_equation:correspondence_principle}
\begin{formula}{ehrenfest_theorem}
\desc{Ehrenfesttheorem}{applies to both pictures}{}
\desc{Ehrenfest theorem}{applies to both pictures}{}
\desc[german]{Ehrenfest-Theorem}{gilt für beide Bilder}{}
\eq{
\odv{}{t} \braket{\hat{A}} = \frac{1}{i\hbar}\braket{[\hat{A},\hat{H}]} + \Braket{\pdv{\hat{A}}{t}}
}
\end{formula}
\begin{formula}{ehrenfest_theorem_x}
\desc{}{Example for $x$}{}
\desc[german]{}{Beispiel für $x$}{}
\desc{Ehrenfest theorem example}{Example for $x$}{}
\desc[german]{Ehrenfest-Theorem Beispiel}{Beispiel für $x$}{}
\eq{m\odv[2]{}{t}\braket{x} = -\braket{\nabla V(x)} = \braket{F(x)}}
\end{formula}
% \eq{Time evolution}{\hat{H}\ket{\psi} = E\ket{\psi}}{sg_time}
@ -382,7 +390,26 @@
\begin{formula}{c_a_matrices}
\desc{Matrix forms}{}{}
\desc[german]{Matrix-Form}{}{}
\eq{\TODO{TODO}}
\eq{
\hat{n} &= \begin{pmatrix}
0 & 0 & 0 & 0 \\
0 & 1 & 0 & 0 \\
0 & 0 & \ddots & 0 \\
0 & 0 & 0 & N
\end{pmatrix} \\
\hat{a} &= \begin{pmatrix}
0 & \sqrt{1} & 0 & 0 \\
0 & 0 & \ddots & 0 \\
0 & 0 & 0 & \sqrt{N} \\
0 & 0 & 0 & 0
\end{pmatrix} \\
\hat{a}^\dagger &= \begin{pmatrix}
0 & 0 & 0 & 0 \\
\sqrt{1} & 0 & 0 & 0 \\
0 & \ddots & 0 & 0 \\
0 & 0 & \sqrt{N} & 0
\end{pmatrix}
}
\end{formula}
\Subsubsection[
@ -419,6 +446,21 @@
\eng{Angular momentum}
\ger{Drehmoment}
]{angular_momentum}
\Subsection[
\eng{Aharanov-Bohm effect}
\ger{Aharanov-Bohm Effekt}
]{aharanov_bohm}
\begin{formula}{phase}
\desc{Acquired phase}{Electron along a closed loop aquires a phase proportional to the enclosed magnetic flux}{}
\desc[german]{Erhaltene Phase}{Elektron entlang eines geschlossenes Phase erhält eine Phase die proportional zum eingeschlossenen magnetischem Fluss ist}{}
\eq{\delta = \frac{2 e}{\hbar} \oint \vec{A}\cdot \d\vec{s} = \frac{2 e}{\hbar} \Phi}
\end{formula}
\TODO{replace with loop intergral symbol and add more info}
\Section[
\eng{Periodic potentials}
\ger{Periodische Potentiale}
]{periodic}
\begin{formula}{bloch_waves}
\desc{Bloch waves}{
Solve the stat. SG in periodic potential with period
@ -435,17 +477,6 @@
\eq{\psi_k(\vec{r}) = e^{i \vec{k}\cdot \vec{r}} \cdot u_{\vec{k}}(\vec{r})}
\end{formula}
\Subsection[
\eng{Aharanov-Bohm effect}
\ger{Aharanov-Bohm Effekt}
]{aharanov_bohm}
\begin{formula}{phase}
\desc{Acquired phase}{Electron along a closed loop aquires a phase proportional to the enclosed magnetic flux}{}
\desc[german]{Erhaltene Phase}{Elektron entlang eines geschlossenes Phase erhält eine Phase die proportional zum eingeschlossenen magnetischem Fluss ist}{}
\eq{\delta = \frac{2 e}{\hbar} \oint \vec{A}\cdot \d\vec{s} = \frac{2 e}{\hbar} \Phi}
\end{formula}
\TODO{replace with loop intergral symbol and add more info}
\Section[
\eng{Symmetries}
@ -488,7 +519,7 @@
\eq{H &= \underbrace{\hbar\omega_c \hat{a}^\dagger \hat{a}}_\text{\GT{field}}
+ \underbrace{\hbar\omega_\text{a} \frac{\hat{\sigma}_z}{2}}_\text{\GT{atom}}
+ \underbrace{\frac{\hbar\Omega}{2} \hat{E} \hat{S}}_\text{int} \\
\shortintertext{\GT{after} \hyperref[eq:qm:other:RWS]{RWA}:} \\
\shortintertext{\GT{after} \hyperref[eq:qm:other:RWA]{RWA}:} \\
&= \hbar\omega_c \hat{a}^\dagger \hat{a}
+ \hbar\omega_\text{a} \hat{\sigma}^\dagger \hat{\sigma}
+ \frac{\hbar\Omega}{2} (\hat{a}\hat{\sigma^\dagger} + \hat{a}^\dagger \hat{\sigma})
@ -499,10 +530,24 @@
\eng{Other}
\ger{Sonstiges}
]{other}
\begin{formula}{RWS}
\begin{formula}{RWA}
\desc{Rotating Wave Approximation (RWS)}{Rapidly oscilating terms are neglected}{$\omega_\text{L}$ light frequency, $\omega_0$ transition frequency}
\desc[german]{Rotating Wave Approximation / Drehwellennäherung (RWS)}{Schnell oscillierende Terme werden vernachlässigt}{$\omega_\text{L}$ Frequenz des Lichtes, $\omega_0$ Übergangsfrequenz}
\eq{\Delta\omega \coloneq \abs{\omega_0 - \omega_\text{L}} \ll \abs{\omega_0 + \omega_\text{L}} \approx 2\omega_0}
\end{formula}
\begin{formula}{slater_det}
\desc{Slater determinant}{Construction of a fermionic (antisymmetric) many-particle wave function from single-particle wave functions}{}
\desc[german]{Slater Determinante}{Konstruktion einer fermionischen (antisymmetrischen) Vielteilchen Wellenfunktion aus ein-Teilchen Wellenfunktionen}{}
\eq{
\Psi(q_1, \dots, q_N) = \frac{1}{\sqrt{N!}}
\begin{vmatrix}
\phi_a(q_1) & \phi_a(q_2) & \cdots & \phi_a(q_N) \\
\phi_b(q_1) & \phi_b(q_2) & \cdots & \phi_b(q_N) \\
\vdots & \vdots & \ddots & \vdots \\
\phi_z(q_1) & \phi_z(q_2) & \cdots & \phi_z(q_N)
\end{vmatrix}
}
\end{formula}

0
src/svgs/convertToPdf.sh Normal file → Executable file
View File

8
src/topo.tex
View File

@ -67,7 +67,6 @@
\eq{C_n = \frac{1}{2\pi} \oint \d \vec{S}\ \cdot \vec{\Omega}_n(\vec{R})}
\end{formula}
\TODO{Hall conductance of 2D band insulator (lecture 4 revision)}
\begin{formula}{hall_conductance}
\desc{Hall conductance of a 2D band insulator}{}{}
\desc[german]{Hall-Leitfähigkeit eines 2D Band-Isolators}{}{}
@ -75,6 +74,9 @@
\end{formula}
\begin{ttext}
\eng{A 2D insulator with a non-zero Chern number is called a \textbf{topological insulator}}
\eng{A 2D insulator with a non-zero Chern number is called a \textbf{topological insulator}.}
\ger{Ein 2D Isolator mit einer Chernzahl ungleich 0 wird \textbf{topologischer Isolator} genannt.}
\end{ttext}

124
src/util/environments.tex
View File

@ -27,12 +27,12 @@
% 3: fqname of a translation that holds the explanation
\newcommand{\NameWithExplanation}[3][\descwidth]{
\begin{minipage}{#1}
\iftranslation{#2}{
\IfTranslationExists{#2}{
\raggedright
\gt{#2}
}{}
\iftranslation{#3}{
\\ {\color{dark1} \gt{#3}}
\GT{#2}
}{NO NAME}
\IfTranslationExists{#3}{
\\ {\color{dark1} \GT{#3}}
}{}
\end{minipage}
}
@ -45,10 +45,10 @@
\begin{minipage}{#1}
% \vspace{-\baselineskip} % remove the space that comes from starting a new paragraph
#2
\noindent\iftranslation{#3}{
\noindent\IfTranslationExists{#3}{
\begingroup
\color{dark1}
\gt{#3}
\GT{#3}
% \edef\temp{\GT{#1_defs}}
% \expandafter\StrSubstitute\expandafter{\temp}{:}{\\}
\endgroup
@ -75,7 +75,7 @@
}
\newcommand{\insertEquation}[2]{
\NameLeftContentRight{#1}{
\NameLeftContentRight{\fqname:#1}{
\begin{align}
\label{eq:\fqname:#1}
#2
@ -84,7 +84,7 @@
}
\newcommand{\insertFLAlign}[2]{ % eq name, #cols, eq
\NameLeftContentRight{#1}{%
\NameLeftContentRight{\fqname:#1}{%
\begin{flalign}%
% dont place label when one is provided
% \IfSubStringInString{label}\unexpanded{#3}{}{
@ -96,7 +96,7 @@
}
\newcommand{\insertAlignedAt}[3]{ % eq name, #cols, eq
\NameLeftContentRight{#1}{%
\NameLeftContentRight{\fqname:#1}{%
\begin{alignat}{#2}%
% dont place label when one is provided
% \IfSubStringInString{label}\unexpanded{#3}{}{
@ -108,15 +108,16 @@
}
\newcommand\luaexpr[1]{\directlua{tex.sprint(#1)}}
% 1: fqname
% 2: file path
% 3: equation
% [1]: width
% 2: fqname
% 3: file path
% 4: equation
\newcommand{\insertEquationWithFigure}[4][0.55]{
\par\noindent\ignorespaces
% \textcolor{gray}{\hrule}
\vspace{0.5\baselineskip}
\begin{minipage}{#1\textwidth}
\NameWithExplanation[\textwidth]{#2}{#2_desc}
\NameWithExplanation[\textwidth]{\fqname:#2}{#2_desc}
% TODO: why is this ignored
\vspace{1.0cm}
% TODO: fix box is too large without 0.9
@ -171,11 +172,11 @@
}
% 1: any content
\newcommand{\content}[1]{
\NameLeftContentRight{#1}{##1}
\NameLeftContentRight{\fqname:#1}{##1}
}
% 1: content for the ttext environment
\newcommand{\ttxt}[1]{
\NameLeftContentRight{#1}{
\NameLeftContentRight{\fqname:#1}{
\begin{ttext}[#1:desc]
##1
\end{ttext}
@ -188,25 +189,92 @@
%
% QUANTITY
%
\newenvironment{quantity}[5]{
% key, symbol, si unit, si base units, comment (key to translation)
% units: siunitx units arguments, possibly chained by '='
% returns: 1\si{unit1} = 1\si{unit2} = ...
\directlua{
function split_and_print_units(units)
if units == nil then
tex.print("1")
return
end
local parts = {}
for part in string.gmatch(units, "[^=]+") do
table.insert(parts, part)
end
local result = ""
for i, unit in ipairs(parts) do
if i > 1 then result = result .. " = " end
result = result .. "\\SI{1}{" .. unit .. "}"
end
tex.print(result)
end
}
\newenvironment{quantity}[4]{
% key, symbol, si unit(s), comment (key to global translation)
\newcommand{\desc}[3][english]{
% language, name, description
\DT[qty:#1]{}{##1}{##2}
% \DT[qty:#1]{##1}{##2}
% \ifblank{##3}{}{\DT[qty:#1_desc]{##1}{##3}}
\DT[qty:#1]{##1}{##2}
\ifblank{##3}{}{\DT[qty:#1_desc]{##1}{##3}}
}
\edef\qtyname{#1}
\edef\qtysign{#2}
\edef\qtyunit{#3}
\edef\qtybaseunits{#4}
\edef\qtycomment{#5}
% TODO put these in long term key - value storage for generating a full table and global referenes \qtyRef
% for references, there needs to be a label somwhere
\edef\qtyname{qty:#1}
\edef\qtydesc{qty:#1_desc}
\def\qtysymbol{#2}
\def\qtyunits{#3}
\edef\qtycomment{#4}
}
{
Quantity: \expandafter\GT\expandafter{qty:\qtyname}: \GT{qty:\qtyname_desc} \\
$\qtysign$ $[\SI{\qtyunit}] = [\SI{\qtybaseunits}]$ - \qtycomment \\
\NameLeftContentRight{\qtyname}{
\begingroup
Symbol: $\qtysymbol$
\IfTranslationExists{\qtydesc}{
\\Description: \GT{\qtydesc}
}{}
\\Unit: $\directlua{split_and_print_units([[\qtyunits]])}$
\expandafter\IfTranslationExists\expandafter\qtycomment{
\\Comment: \GT\qtycomment
}{\\No comment \color{gray}}
\label{\qtyname}
\endgroup
}
\ignorespacesafterend
% for TOC
\refstepcounter{quantity}%
\addquantity{\expandafter\gt\expandafter{\qtyname}}%
% \noindent\textbf{My Environment \themyenv: #1}\par%
}
\newcounter{quantity}
\Eng[list_of_quantitites]{List of quantitites}
\Ger[list_of_quantitites]{Liste von Größen}
\newcommand{\listofquantities}{%
\section*{\GT{list_of_quantitites}}%
\addcontentsline{toc}{section}{\GT{list_of_quantitites}}%
\par\noindent\hrule\par\vspace{0.5\baselineskip}\@starttoc{myenv}%
}
\newcommand{\addquantity}[1]{\addcontentsline{quantity}{subsection}{\protect\numberline{\themyenv}#1}}
% Custon environment with table of contents, requires etoolbox?
% Define a custom list
\newcommand{\listofmyenv}{%
\section*{List of My Environments}%
\addcontentsline{toc}{section}{List of My Environments}%
\par\noindent\hrule\par\vspace{0.5\baselineskip}\@starttoc{myenv}%
}
\newcommand{\addmyenv}[1]{\addcontentsline{myenv}{subsection}{\protect\numberline{\themyenv}#1}}
% Define the custom environment
\newcounter{myenv}
\newenvironment{myenv}[1]{%
\refstepcounter{myenv}%
\addmyenv{#1}%
\noindent\textbf{My Environment \themyenv: #1}\par%
}{\par\vspace{0.5\baselineskip}}
@ -226,7 +294,7 @@
\directlua{
local cases = {
pdf = "eq:pt:distributions:pdf",
pmf = "eq:pt:distributions:pdf",
pmf = "eq:pt:distributions:pmf",
cdf = "eq:pt:distributions:cdf",
mean = "eq:pt:mean",
variance = "eq:pt:variance"

2
src/util/macros.tex
View File

@ -4,7 +4,9 @@
\def\Grad{\vec{\nabla}}
\def\Div{\vec{\nabla} \cdot}
\def\Rot{\vec{\nabla} \times}
% common vectors
\def\vecr{\vec{r}}
\def\vecx{\vec{x}}
\def\kB{k_\text{B}}
\def\EFermi{E_\text{F}}

20
src/util/translation.tex
View File

@ -18,11 +18,17 @@
\newcommand{\gt}[1]{\expandafter\GetTranslation\expandafter{\fqname:#1}}
\newcommand{\GT}[1]{\expandafter\GetTranslation\expandafter{#1}}
\newcommand{\IfTranslationExists}{
% \IfTranslation{\languagename}
\IfTranslation{english} % only check english. All translations must be defined for english
\newcommand{\IfTranslationExists}[1]{
% \IfTranslation{english}{#1}%{#2}{#3} % only check english. All translations must be defined for english
% \edef\arg{#1}
\def\tempiftranslation{\IfTranslation{english}}
\expandafter\tempiftranslation\expandafter{#1} % only check english. All translations must be defined for english
% {S\color{red}\arg END}
% \IfTranslation{english}{\arg} % only check english. All translations must be defined for english
}
\newcommand{\iftranslation}[3]{
\IfTranslationExists{\fqname:#1}{#2}{#3}
}
\newcommand{\iftranslation}[1]{\expandafter\IfTranslationExists\expandafter{\fqname:#1}}
% Define a translation and also make the fallback if it is the english translation
% 1: lang, 2: key, 3: translation
@ -46,11 +52,13 @@
}
}
}
\newcommand{\DT}[3][\fqname]{
% Define a new translation
% [1]: key, 2: lang, 3: translation
\newcommand{\DT}[3][dummy]{
\ifstrempty{#3}{}{ % dont add empty translations so that the fallback will be used instead
% hack because using expandafter on the second arg didnt work
\def\tempaddtranslation{\addtranslationcustom{#2}}
\ifstrequal{#1}{\fqname}{
\ifstrequal{#1}{dummy}{
\expandafter\tempaddtranslation\expandafter{\fqname}{#3}
}{
\expandafter\tempaddtranslation\expandafter{#1}{#3}