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refactor referencing

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matthias@quintern.xyz 2025-02-25 23:26:19 +01:00
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32 changed files with 623 additions and 390 deletions
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3
src/.latexmkrc
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@ -5,12 +5,13 @@ $out_dir = '../out';
# Set lualatex as the default engine # Set lualatex as the default engine
$pdf_mode = 1; # Enable PDF generation mode $pdf_mode = 1; # Enable PDF generation mode
# $pdflatex = 'lualatex --interaction=nonstopmode --shell-escape' # $pdflatex = 'lualatex --interaction=nonstopmode --shell-escape'
$lualatex = 'lualatex %O --interaction=nonstopmode --shell-escape %S' $lualatex = 'lualatex %O --interaction=nonstopmode --shell-escape %S';
# Additional options for compilation # Additional options for compilation
# '-verbose', # '-verbose',
# '-file-line-error', # '-file-line-error',
ensure_path('TEXINPUTS', './pkg');
# Quickfix-like filtering (warnings to ignore) # Quickfix-like filtering (warnings to ignore)
# @warnings_to_filter = ( # @warnings_to_filter = (
# qr/Underfull \\hbox/, # qr/Underfull \\hbox/,

28
src/ch/el.tex
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@ -24,7 +24,7 @@
\end{formula} \end{formula}
\begin{formula}{activity} \begin{formula}{activity}
\desc{Activity}{relative activity}{\QtyRef{chemical_potential}, \QtyRef{standard_chemical_potential}, \ConstRef{universal_gas}, \QtyRef{temperature}} \desc{Activity}{relative activity}{\QtyRef{chemical_potential}, \fRef{::standard_chemical_potential}, \ConstRef{universal_gas}, \QtyRef{temperature}}
\desc[german]{Aktivität}{Relative Aktivität}{} \desc[german]{Aktivität}{Relative Aktivität}{}
\quantity{a}{}{s} \quantity{a}{}{s}
\eq{a_i = \Exp{\frac{\mu_i-\mu_i^\theta}{RT}}} \eq{a_i = \Exp{\frac{\mu_i-\mu_i^\theta}{RT}}}
@ -147,13 +147,13 @@
\begin{formula}{nernst_equation} \begin{formula}{nernst_equation}
\desc{Nernst equation}{Electrode potential for a half-cell reaction}{\QtyRef{electrode_potential}, $E^\theta$ \secEqRef{standard_cell_potential}, \ConstRef{universal_gas}, \ConstRef{temperature}, $z$ \qtyRef{charge_number}, \ConstRef{faraday}, \QtyRef{activity}, \QtyRef{stoichiometric_coefficient}} \desc{Nernst equation}{Electrode potential for a half-cell reaction}{\QtyRef{electrode_potential}, $E^\theta$ \fRef{::standard_cell_potential}, \ConstRef{universal_gas}, \ConstRef{temperature}, $z$ \qtyRef{charge_number}, \ConstRef{faraday}, \QtyRef{activity}, \QtyRef{stoichiometric_coefficient}}
\desc[german]{Nernst-Gleichung}{Elektrodenpotential für eine Halbzellenreaktion}{} \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}}}} \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} \end{formula}
\begin{formula}{cell_efficiency} \begin{formula}{cell_efficiency}
\desc{Thermodynamic cell efficiency}{}{$P$ \fqEqRef{ed:el:power}} \desc{Thermodynamic cell efficiency}{}{$P$ \fRef{ed:el:power}}
\desc[german]{Thermodynamische Zelleffizienz}{}{} \desc[german]{Thermodynamische Zelleffizienz}{}{}
\eq{ \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{obtained}}{P_\text{maximum}} = \frac{E_\text{cell}}{E_\text{cell,rev}} & & \text{\gt{galvanic}} \\
@ -312,8 +312,8 @@
\ger{Massentransport} \ger{Massentransport}
]{mass} ]{mass}
\begin{formula}{concentration_overpotential} \begin{formula}{concentration_overpotential}
\desc{Concentration overpotential}{Due to concentration gradient near the electrode, the ions need to \hyperref[f:ch:el:ion_cond:diffusion]{diffuse} to the electrode before reacting}{\ConstRef{universal_gas}, \QtyRef{temperature}, $\c_{0/\txS}$ ion concentration in the electrolyte / at the double layer, $z$ \qtyRef{charge_number}, \ConstRef{faraday}} \desc{Concentration overpotential}{Due to concentration gradient near the electrode, the ions need to \fRef[diffuse]{ch:el:ion_cond:diffusion} to the electrode before reacting}{\ConstRef{universal_gas}, \QtyRef{temperature}, $\c_{0/\txS}$ ion concentration in the electrolyte / at the double layer, $z$ \qtyRef{charge_number}, \ConstRef{faraday}}
\desc[german]{Konzentrationsüberspannung}{Durch einen Konzentrationsgradienten an der Elektrode müssen Ionen erst zur Elektrode \hyperref[f:ch:el:ion_cond:diffusion]{diffundieren}, bevor sie reagieren können}{} \desc[german]{Konzentrationsüberspannung}{Durch einen Konzentrationsgradienten an der Elektrode müssen Ionen erst zur Elektrode \fRef[diffundieren]{ch:el:ion_cond:diffusion}, bevor sie reagieren können}{}
\eq{ \eq{
\eta_\text{conc,anodic} &= -\frac{RT}{\alpha \,zF} \ln \left(\frac{c_\text{red}^0}{c_\text{red}^\txS}\right) \\ \eta_\text{conc,anodic} &= -\frac{RT}{\alpha \,zF} \ln \left(\frac{c_\text{red}^0}{c_\text{red}^\txS}\right) \\
\eta_\text{conc,cathodic} &= -\frac{RT}{(1-\alpha) zF} \ln \left(\frac{c_\text{ox}^0}{c_\text{ox}^\txS}\right) \eta_\text{conc,cathodic} &= -\frac{RT}{(1-\alpha) zF} \ln \left(\frac{c_\text{ox}^0}{c_\text{ox}^\txS}\right)
@ -321,7 +321,7 @@
\end{formula} \end{formula}
\begin{formula}{diffusion_overpotential} \begin{formula}{diffusion_overpotential}
\desc{Diffusion overpotential}{Due to mass transport limitations}{$j_\infty$ \secEqRef{limiting_current}, $j_\text{meas}$ measured \qtyRef{current_density}, \ConstRef{universal_gas}, \QtyRef{temperature}, $n$ \qtyRef{charge_number}, \ConstRef{faraday}} \desc{Diffusion overpotential}{Due to mass transport limitations}{$j_\infty$ \fRef{::limiting_current}, $j_\text{meas}$ measured \qtyRef{current_density}, \ConstRef{universal_gas}, \QtyRef{temperature}, $n$ \qtyRef{charge_number}, \ConstRef{faraday}}
\desc[german]{Diffusionsüberspannung}{Durch Limit des Massentransports}{} \desc[german]{Diffusionsüberspannung}{Durch Limit des Massentransports}{}
% \eq{\eta_\text{diff} = \frac{RT}{nF} \ln \left( \frac{\cfrac{c^\txs_\text{ox}}{c^0_\text{ox}}}{\cfrac{c^\txs_\text{red}}{c^0_\text{red}}} \right)} % \eq{\eta_\text{diff} = \frac{RT}{nF} \ln \left( \frac{\cfrac{c^\txs_\text{ox}}{c^0_\text{ox}}}{\cfrac{c^\txs_\text{red}}{c^0_\text{red}}} \right)}
\eq{\eta_\text{diff} = \frac{RT}{nF} \Ln{\frac{j_\infty}{j_\infty - j_\text{meas}}}} \eq{\eta_\text{diff} = \frac{RT}{nF} \Ln{\frac{j_\infty}{j_\infty - j_\text{meas}}}}
@ -424,7 +424,7 @@
\end{formula} \end{formula}
\begin{formula}{limiting_current} \begin{formula}{limiting_current}
\desc{(Limiting) current density}{}{$n$ \QtyRef{charge_number}, \ConstRef{faraday}, $c^0$ \GT{c_bulk}, $D$ \qtyRef{diffusion_coefficient}, $\delta_\text{diff}$ \secEqRef{diffusion_layer_thickness}} \desc{(Limiting) current density}{}{$n$ \QtyRef{charge_number}, \ConstRef{faraday}, $c^0$ \GT{c_bulk}, $D$ \qtyRef{diffusion_coefficient}, $\delta_\text{diff}$ \fRef{::diffusion_layer_thickness}}
% \desc[german]{Limitierender Strom}{}{} % \desc[german]{Limitierender Strom}{}{}
\eq{ \eq{
\abs{j} &= nFD \frac{c^0-c^\txS}{\delta_\text{diff}} \abs{j} &= nFD \frac{c^0-c^\txS}{\delta_\text{diff}}
@ -434,14 +434,14 @@
\end{formula} \end{formula}
\begin{formula}{relation?} \begin{formula}{relation?}
\desc{Current - concentration relation}{}{$c^0$ \GT{c_bulk}, $c^\txS$ \GT{c_surface}, $j$ \secEqRef{limiting_current}} \desc{Current - concentration relation}{}{$c^0$ \GT{c_bulk}, $c^\txS$ \GT{c_surface}, $j$ \fRef{::limiting_current}}
\desc[german]{Strom - Konzentrationsbeziehung}{}{} \desc[german]{Strom - Konzentrationsbeziehung}{}{}
\eq{\frac{j}{j_\infty} = 1 - \frac{c^\txS}{c^0}} \eq{\frac{j}{j_\infty} = 1 - \frac{c^\txS}{c^0}}
\end{formula} \end{formula}
\begin{formula}{kinetic_current} \begin{formula}{kinetic_current}
\desc{Kinetic current density}{}{$j_\text{meas}$ measured \qtyRef{current_density}, $j_\infty$ \secEqRef{limiting_current}} \desc{Kinetic current density}{}{$j_\text{meas}$ measured \qtyRef{current_density}, $j_\infty$ \fRef{::limiting_current}}
\desc[german]{Kinetische Stromdichte}{}{$j_\text{meas}$ gemessene \qtyRef{current_density}, $j_\infty$ \secEqRef{limiting_current}} \desc[german]{Kinetische Stromdichte}{}{$j_\text{meas}$ gemessene \qtyRef{current_density}, $j_\infty$ \fRef{::limiting_current}}
\eq{j_\text{kin} = \frac{j_\text{meas} j_\infty}{j_\infty - j_\text{meas}}} \eq{j_\text{kin} = \frac{j_\text{meas} j_\infty}{j_\infty - j_\text{meas}}}
\end{formula} \end{formula}
@ -452,10 +452,10 @@
\begin{formula}{butler_volmer} \begin{formula}{butler_volmer}
\desc{Butler-Volmer equation}{Reaction kinetics near the equilibrium potentential} \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, $\text{rf}$ \secEqRef{roughness_factor}} {$j$ \qtyRef{current_density}, $j_0$ exchange current density, $\eta$ \fRef{ch:el:kin:overpotential}, \QtyRef{temperature}, $z$ \qtyRef{charge_number}, \ConstRef{faraday}, \ConstRef{universal_gas}, $\alpha_{\txC/\txA}$ cathodic/anodic charge transfer coefficient, $\text{rf}$ \fRef{::roughness_factor}}
%Current through an electrode iof a unimolecular redox reaction with both anodic and cathodic reaction occuring on the same electrode %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} \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, $\text{rf}$ \secEqRef{roughness_factor}} {$j$ \qtyRef{current_density}, $j_0$ Austauschstromdichte, $\eta$ \fRef{ch:el:kin:overpotential}, \QtyRef{temperature}, $z$ \qtyRef{charge_number}, \ConstRef{faraday}, \ConstRef{universal_gas}, $\alpha_{\txC/\txA}$ Ladungstransferkoeffizient an der Kathode/Anode, $\text{rf}$ \fRef{::roughness_factor}}
\begin{gather} \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] 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}} \intertext{\GT{with}}
@ -512,7 +512,7 @@
\end{formula} \end{formula}
\begin{formula}{rhe} \begin{formula}{rhe}
\desc{Reversible hydrogen electrode (RHE)}{RHE Potential does not change with the pH value}{$E^0\equiv \SI{0}{\volt}$, \QtyRef{activity}, \QtyRef{pressure}, \GT{see} \fqEqRef{ch:el:cell:nernst_equation}} \desc{Reversible hydrogen electrode (RHE)}{RHE Potential does not change with the pH value}{$E^0\equiv \SI{0}{\volt}$, \QtyRef{activity}, \QtyRef{pressure}, \GT{see} \fRef{ch:el:cell:nernst_equation}}
\desc[german]{Reversible Wasserstoffelektrode (RHE)}{Potential ändert sich nicht mit dem pH-Wert}{} \desc[german]{Reversible Wasserstoffelektrode (RHE)}{Potential ändert sich nicht mit dem pH-Wert}{}
\eq{ \eq{
E_\text{RHE} &= E^0 + \frac{RT}{F} \Ln{\frac{a_{\ce{H^+}}}{p_{\ce{H2}}}} E_\text{RHE} &= E^0 + \frac{RT}{F} \Ln{\frac{a_{\ce{H^+}}}{p_{\ce{H2}}}}
@ -638,7 +638,7 @@
\end{formula} \end{formula}
\begin{formula}{limiting_current} \begin{formula}{limiting_current}
\desc{Limiting current density}{for a \abbrRef{rde}}{$n$ \QtyRef{charge_number}, \ConstRef{faraday}, $c^0$ \GT{c_bulk}, $D$ \qtyRef{diffusion_coefficient}, $\delta_\text{diff}$ \secEqRef{diffusion_layer_thickness}, $\nu$ \qtyRef{kinematic_viscosity}, \QtyRef{angular_frequency}} \desc{Limiting current density}{for a \abbrRef{rde}}{$n$ \QtyRef{charge_number}, \ConstRef{faraday}, $c^0$ \GT{c_bulk}, $D$ \qtyRef{diffusion_coefficient}, $\delta_\text{diff}$ \fRef{::diffusion_layer_thickness}, $\nu$ \qtyRef{kinematic_viscosity}, \QtyRef{angular_frequency}}
% \desc[german]{Limitierender Strom}{}{} % \desc[german]{Limitierender Strom}{}{}
\eq{j_\infty = nFD \frac{c^0}{\delta_\text{diff}} = \frac{1}{1.61} nFD^{\frac{2}{3}} v^{\frac{-1}{6}} c^0 \sqrt{\omega}} \eq{j_\infty = nFD \frac{c^0}{\delta_\text{diff}} = \frac{1}{1.61} nFD^{\frac{2}{3}} v^{\frac{-1}{6}} c^0 \sqrt{\omega}}
\end{formula} \end{formula}

4
src/cm/charge_transport.tex
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@ -63,8 +63,8 @@
\ger{Boltzmann-Transport} \ger{Boltzmann-Transport}
]{boltzmann} ]{boltzmann}
\begin{ttext} \begin{ttext}
\eng{Semiclassical description using a probability distribution (\fqEqRef{stat:todo:fermi_dirac}) to describe the particles.} \eng{Semiclassical description using a probability distribution (\fRef{stat:todo:fermi_dirac}) to describe the particles.}
\ger{Semiklassische Beschreibung, benutzt eine Wahrscheinlichkeitsverteilung (\fqEqRef{stat:todo:fermi_dirac}).} \ger{Semiklassische Beschreibung, benutzt eine Wahrscheinlichkeitsverteilung (\fRef{stat:todo:fermi_dirac}).}
\end{ttext} \end{ttext}
\begin{formula}{boltzmann_transport} \begin{formula}{boltzmann_transport}
\desc{Boltzmann Transport equation}{for charge transport}{$f$ \ref{stat:todo:fermi-dirac}} \desc{Boltzmann Transport equation}{for charge transport}{$f$ \ref{stat:todo:fermi-dirac}}

8
src/cm/cm.tex
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@ -11,8 +11,8 @@
\eq{D(E) = \frac{1}{V}\sum_{i=1}^{N} \delta(E-E(\vec{k_i}))} \eq{D(E) = \frac{1}{V}\sum_{i=1}^{N} \delta(E-E(\vec{k_i}))}
\end{formula} \end{formula}
\begin{formula}{dos_parabolic} \begin{formula}{dos_parabolic}
\desc{Density of states for parabolic dispersion}{Applies to \fqSecRef{cm:egas}}{} \desc{Density of states for parabolic dispersion}{Applies to \fRef{cm:egas}}{}
\desc[german]{Zustandsdichte für parabolische Dispersion}{Bei \fqSecRef{cm:egas}}{} \desc[german]{Zustandsdichte für parabolische Dispersion}{Bei \fRef{cm:egas}}{}
\eq{ \eq{
D_1(E) &= \frac{1}{2\sqrt{c_k(E-E_0)}} && (\text{1D}) \\ D_1(E) &= \frac{1}{2\sqrt{c_k(E-E_0)}} && (\text{1D}) \\
D_2(E) &= \frac{\pi}{2c_k} && (\text{2D}) \\ D_2(E) &= \frac{\pi}{2c_k} && (\text{2D}) \\
@ -65,8 +65,8 @@
\ger{Debye-Modell} \ger{Debye-Modell}
]{debye} ]{debye}
\begin{ttext} \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.} \eng{Atoms behave like coupled \fRef[quantum harmonic oscillators]{sec:qm:hosc}. 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. } \ger{Atome verhalten sich wie gekoppelte \fRef[quantenmechanische harmonische Oszillatoren]{sec:qm:hosc}. Die endliche Ausdehnung des Körpers führt zu periodischen Randbedingungen. }
\end{ttext} \end{ttext}

18
src/cm/crystal.tex
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@ -135,8 +135,8 @@
} }
\end{formula} \end{formula}
\begin{formula}{bcc} \begin{formula}{bcc}
\desc{Body centered cubic (BCC)}{Reciprocal: \fqEqRef{cm:bravais:fcc}}{\QtyRef{lattice_constant}} \desc{Body centered cubic (BCC)}{Reciprocal: \fRef{::fcc}}{\QtyRef{lattice_constant}}
\desc[german]{Kubisch raumzentriert (BCC)}{Reziprok: \fqEqRef{cm:bravais:fcc}}{} \desc[german]{Kubisch raumzentriert (BCC)}{Reziprok: \fRef{::fcc}}{}
\eq{ \eq{
\vec{a}_{1}=\frac{a}{2} \begin{pmatrix} -1\\1\\1 \end{pmatrix},\, \vec{a}_{1}=\frac{a}{2} \begin{pmatrix} -1\\1\\1 \end{pmatrix},\,
\vec{a}_{2}=\frac{a}{2} \begin{pmatrix} 1\\-1\\1 \end{pmatrix},\, \vec{a}_{2}=\frac{a}{2} \begin{pmatrix} 1\\-1\\1 \end{pmatrix},\,
@ -145,8 +145,8 @@
\end{formula} \end{formula}
\begin{formula}{fcc} \begin{formula}{fcc}
\desc{Face centered cubic (FCC)}{Reciprocal: \fqEqRef{cm:bravais:bcc}}{\QtyRef{lattice_constant}} \desc{Face centered cubic (FCC)}{Reciprocal: \fRef{::bcc}}{\QtyRef{lattice_constant}}
\desc[german]{Kubisch flächenzentriert (FCC)}{Reziprok: \fqEqRef{cm:bravais:bcc}}{} \desc[german]{Kubisch flächenzentriert (FCC)}{Reziprok: \fRef{::bcc}}{}
\eq{ \eq{
\vec{a}_{1}=\frac{a}{2} \begin{pmatrix} 0\\1\\1 \end{pmatrix},\, \vec{a}_{1}=\frac{a}{2} \begin{pmatrix} 0\\1\\1 \end{pmatrix},\,
\vec{a}_{2}=\frac{a}{2} \begin{pmatrix} 1\\0\\1 \end{pmatrix},\, \vec{a}_{2}=\frac{a}{2} \begin{pmatrix} 1\\0\\1 \end{pmatrix},\,
@ -158,8 +158,8 @@
\desc{Diamond lattice}{}{} \desc{Diamond lattice}{}{}
\desc[german]{Diamantstruktur}{}{} \desc[german]{Diamantstruktur}{}{}
\ttxt{ \ttxt{
\eng{\fqEqRef{cm:bravais:fcc} with basis $\begin{pmatrix} 0 & 0 & 0 \end{pmatrix}$ and $\begin{pmatrix} \frac{1}{4} & \frac{1}{4} & \frac{1}{4} \end{pmatrix}$} \eng{\fRef{:::fcc} with basis $\begin{pmatrix} 0 & 0 & 0 \end{pmatrix}$ and $\begin{pmatrix} \frac{1}{4} & \frac{1}{4} & \frac{1}{4} \end{pmatrix}$}
\ger{\fqEqRef{cm:bravais:fcc} mit Basis $\begin{pmatrix} 0 & 0 & 0 \end{pmatrix}$ und $\begin{pmatrix} \frac{1}{4} & \frac{1}{4} & \frac{1}{4} \end{pmatrix}$} \ger{\fRef{:::fcc} mit Basis $\begin{pmatrix} 0 & 0 & 0 \end{pmatrix}$ und $\begin{pmatrix} \frac{1}{4} & \frac{1}{4} & \frac{1}{4} \end{pmatrix}$}
} }
\end{formula} \end{formula}
\begin{formula}{zincblende} \begin{formula}{zincblende}
@ -167,8 +167,8 @@
\desc[german]{Zinkblende-Struktur}{}{} \desc[german]{Zinkblende-Struktur}{}{}
\ttxt{ \ttxt{
\includegraphics[width=0.5\textwidth]{img/cm_zincblende.png} \includegraphics[width=0.5\textwidth]{img/cm_zincblende.png}
\eng{Like \fqEqRef{cm:bravais:diamond} but with different species on each basis} \eng{Like \fRef{:::diamond} but with different species on each basis}
\ger{Wie \fqEqRef{cm:bravais:diamond} aber mit unterschiedlichen Spezies auf den Basen} \ger{Wie \fRef{:::diamond} aber mit unterschiedlichen Spezies auf den Basen}
} }
\end{formula} \end{formula}
\begin{formula}{wurtzite} \begin{formula}{wurtzite}
@ -176,7 +176,7 @@
\desc[german]{Wurtzite-Struktur}{hP4}{} \desc[german]{Wurtzite-Struktur}{hP4}{}
\ttxt{ \ttxt{
\includegraphics[width=0.5\textwidth]{img/cm_wurtzite.png} \includegraphics[width=0.5\textwidth]{img/cm_wurtzite.png}
Placeholder \TODO{Placeholder}
} }
\end{formula} \end{formula}

112
src/cm/low_temp.tex
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@ -1,10 +1,8 @@
\def\L{\text{L}} \def\txL{\text{L}}
\def\gl{\text{GL}} \def\gl{\text{GL}}
\def\GL{Ginzburg-Landau } \def\GL{Ginzburg-Landau }
\def\Tcrit{T_\text{c}} \def\Tcrit{T_\text{c}}
\def\Bcrit{B_\text{c}} \def\Bcth{B_\text{c}}
\def\ssc{\text{s}}
\def\ssn{\text{n}}
\Section[ \Section[
\eng{Superconductivity} \eng{Superconductivity}
@ -13,78 +11,116 @@
\begin{ttext} \begin{ttext}
\eng{ \eng{
Materials for which the electric resistance jumps to 0 under a critical temperature $\Tcrit$. Materials for which the electric resistance jumps to 0 under a critical temperature $\Tcrit$.
Below $\Tcrit$ they have perfect conductivity and perfect diamagnetism, up until a critical magnetic field $\Bcrit$. Below $\Tcrit$ they have perfect conductivity and perfect diamagnetism, up until a critical magnetic field $\Bcth$.
\\\textbf{Type I}: Has a single critical magnetic field at which the superconuctor becomes a normal conductor. \\\textbf{Type I}:
\\\textbf{Type II}: Has two critical \\\textbf{Type II}: Has two critical
} }
\ger{ \ger{
Materialien, bei denen der elektrische Widerstand beim unterschreiten einer kritischen Temperatur $\Tcrit$ auf 0 springt. Materialien, bei denen der elektrische Widerstand beim unterschreiten einer kritischen Temperatur $\Tcrit$ auf 0 springt.
Sie verhalten sich dann wie ideale Leiter und ideale Diamagnete, bis zu einem kritischen Feld $\Bcrit$. Sie verhalten sich dann wie ideale Leiter und ideale Diamagnete, bis zu einem kritischen Feld $\Bcth$.
} }
\end{ttext} \end{ttext}
\begin{formula}{type1}
\desc{Type-I superconductor}{}{}
\desc[german]{Typ-I Supraleiter}{}{}
\ttxt{\eng{
Has a single critical magnetic field, $\Bcth$.
\\$B < \Bcth$: \fRef{:::meissner_effect}
\\$B > \Bcth$: Normal conductor
}}
\end{formula}
\begin{formula}{type2}
\desc{Type-II superconductor}{}{}
\desc[german]{Typ-II Supraleiter}{}{}
\ttxt{\eng{
Has a two critical magnetic fields.
\\$B < B_\text{c1}$: \fRef{:::meissner_effect}
\\$B_\text{c1} < B < B_\text{c2}$: \fRef{:::shubnikov_phase}
\\$B > B_\text{c2}$: Normal conductor
}}
\end{formula}
\begin{formula}{perfect_conductor} \begin{formula}{perfect_conductor}
\desc{Perfect conductor}{}{} \desc{Perfect conductor}{}{}
\desc[german]{Ideale Leiter}{}{} \desc[german]{Ideale Leiter}{}{}
\ttxt{ \ttxt{
\eng{ \eng{
In contrast to a superconductor, perfect conductors become diamagnetic only when the external magnetic field is turned on \textbf{after} the material was cooled below the critical temperature. In contrast to a superconductor, perfect conductors become diamagnetic only when the external magnetic field is turned on \textbf{after} the material was cooled below the critical temperature.
(\fqEqRef{ed:fields:mag:induction:lenz}) (\fRef{ed:fields:mag:induction:lenz})
} }
\ger{ \ger{
Im Gegensatz zu einem Supraleiter werden ideale Leiter nur dann diamagnetisch, wenn das externe magnetische Feld \textbf{nach} dem Abkühlen unter die kritische Temperatur eingeschaltet wird. Im Gegensatz zu einem Supraleiter werden ideale Leiter nur dann diamagnetisch, wenn das externe magnetische Feld \textbf{nach} dem Abkühlen unter die kritische Temperatur eingeschaltet wird.
(\fqEqRef{ed:fields:mag:induction:lenz}) (\fRef{ed:fields:mag:induction:lenz})
} }
} }
\end{formula} \end{formula}
\begin{formula}{meissner_effect} \begin{formula}{meissner_effect}
\desc{Meißner-Ochsenfeld effect}{Perfect diamagnetism}{} \desc{Meißner-Ochsenfeld effect}{Perfect diamagnetism}{$\chi=-1$ \qtyRef{magnetic_susceptibility}}
\desc[german]{Meißner-Ochsenfeld Effekt}{Idealer Diamagnetismus}{} \desc[german]{Meißner-Ochsenfeld Effekt}{Perfekter Diamagnetismus}{}
\ttxt{ \ttxt{
\eng{External magnetic field decays exponetially inside the superconductor below a critical temperature and a critical magnetic field.} \eng{External magnetic field decays exponetially inside the superconductor below a critical temperature and a critical magnetic field, path-independant.}
\ger{Externes Magnetfeld fällt im Supraleiter exponentiell unterhalb einer kritischen Temperatur und unterhalb einer kritischen Feldstärke ab.} \ger{Externes Magnetfeld fällt im Supraleiter exponentiell unterhalb einer kritischen Temperatur und unterhalb einer kritischen Feldstärke ab, wegunabhängig.}
} }
\end{formula} \end{formula}
\begin{formula}{condensation_energy}
\desc{Condensation energy}{}{\QtyRef{gibbs_energy}}
\desc[german]{Kondensationsenergie}{}{}
\eq{
\d G &= -S \d T + V \d p - V \vecM \cdot \d\vecB \\
G_\text{con} &= G_\txn(B=0,T) - G_\txs(B=0,T) = \frac{V \Bcth^2(T)}{2\mu_0}
}
\end{formula}
\Subsection[ \Subsection[
\eng{London equations} \eng{London equations}
\ger{London-Gleichungen} \ger{London-Gleichungen}
]{london} ]{london}
\begin{ttext} \begin{ttext}
\eng{ \eng{
Quantitative description of the \fqEqRef{cm:sc:meissner_effect}. Quantitative description of the \fRef{cm:sc:meissner_effect}.
} }
\ger{ \ger{
Quantitative Beschreibung des \fqEqRef{cm:sc:meissner_effect}s. Quantitative Beschreibung des \fRef{cm:sc:meissner_effect}s.
} }
\end{ttext} \end{ttext}
% \begin{formula}{coefficient} % \begin{formula}{coefficient}
% \desc{London-coefficient}{}{} % \desc{London-coefficient}{}{}
% \desc[german]{London-Koeffizient}{}{} % \desc[german]{London-Koeffizient}{}{}
% \eq{\Lambda = \frac{m_\ssc}{n_\ssc q_\ssc^2}} % \eq{\txLambda = \frac{m_\txs}{n_\txs q_\txs^2}}
% \end{formula} % \end{formula}
\Eng[of_sc_particle]{of the superconducting particle}
\Ger[of_sc_particle]{der Supraleitenden Teilchen}
\begin{formula}{first} \begin{formula}{first}
% \vec{j} = \frac{nq\hbar}{m}\Grad S - \frac{nq^2}{m}\vec{A} % \vec{j} = \frac{nq\hbar}{m}\Grad S - \frac{nq^2}{m}\vec{A}
\desc{First London Equation}{}{$\vec{j}$ current density, $n_\ssc$, $m_\ssc$, $q_\ssc$ density, mass and charge of superconduticng particles} \desc{First London Equation}{}{$\vec{j}$ \qtyRef{current_density}, $m_\txs$/$n_\txs$/$q_\txs$ \qtyRef{mass}/\qtyRef{charge_carrier_density}/\qtyRef{charge} \GT{of_sc_particle}, \QtyRef{electric_field}}
\desc[german]{Erste London-Gleichun-}{}{$\vec{j}$ Stromdichte, $n_\ssc$, $m_\ssc$, $q_\ssc$ Dichte, Masse und Ladung der supraleitenden Teilchen} \desc[german]{Erste London-Gleichun-}{}{}
\eq{ \eq{
\pdv{\vec{j}_{\ssc}}{t} = \frac{n_\ssc q_\ssc^2}{m_\ssc}\vec{E} {\color{gray}- \Order{\vec{j}_\ssc^2}} \pdv{\vec{j}_{\txs}}{t} = \frac{n_\txs q_\txs^2}{m_\txs}\vec{\E} {\color{gray}- \Order{\vec{j}_\txs^2}}
% \\{\color{gray} = \frac{q}{m}\Grad \left(\frac{1}{2} \TODO{FActor} \vec{j}^2\right)} % \\{\color{gray} = \frac{q}{m}\Grad \left(\frac{1}{2} \TODO{FActor} \vec{j}^2\right)}
} }
\end{formula} \end{formula}
\begin{formula}{second} \begin{formula}{second}
\desc{Second London Equation}{Describes the \fqEqRef{cm:sc:meissner_effect}}{$\vec{j}$ current density, $n_\ssc$, $m_\ssc$, $q_\ssc$ density, mass and charge of superconduticng particles} \desc{Second London Equation}{Describes the \fRef{cm:sc:meissner_effect}}{$\vec{j}$ \qtyRef{current_density}, $m_\txs$/$n_\txs$/$q_\txs$ \qtyRef{mass}/\qtyRef{charge_carrier_density}/\qtyRef{charge} \GT{of_sc_particle}, \QtyRef{magnetic_field}}
\desc[german]{Zweite London-Gleichung}{Beschreibt den \fqEqRef{cm:sc:meissner_effect}}{$\vec{j}$ Stromdichte, $n_\ssc$, $m_\ssc$, $q_\ssc$ Dichte, Masse und Ladung der supraleitenden Teilchen} \desc[german]{Zweite London-Gleichung}{Beschreibt den \fRef{cm:sc:meissner_effect}}{}
\eq{ \eq{
\Rot \vec{j_\ssc} = -\frac{n_\ssc q_\ssc^2}{m_\ssc} \vec{B} \Rot \vec{j_\txs} = -\frac{n_\txs q_\txs^2}{m_\txs} \vec{B}
} }
\end{formula} \end{formula}
\begin{formula}{penetration_depth} \begin{formula}{penetration_depth}
\desc{London penetration depth}{}{} \desc{London penetration depth}{Depth at which $B$ is $1/\e$ times the value of $B_\text{ext}$}{$m_\txs$/$n_\txs$/$q_\txs$ \qtyRef{mass}/\qtyRef{charge_carrier_density}/\qtyRef{charge} \GT{of_sc_particle}}
\desc[german]{London Eindringtiefe}{}{} \desc[german]{London Eindringtiefe}{Tiefe bei der $B$ das $1/\e$-fache von $B_\text{ext}$ ist}{}
\eq{\lambda_\L = \sqrt{\frac{m_\ssc}{\mu_0 n_\ssc q_\ssc^2}}} \eq{\lambda_\txL = \sqrt{\frac{m_\txs}{\mu_0 n_\txs q_\txs^2}}}
\end{formula}
\begin{formula}{penetration_depth_temp}
\desc{Temperature dependence of \fRef{::penetration_depth}}{}{}
\desc[german]{Temperaturabhängigkeit der \fRef{::penetration_depth}}{}{}
\eq{\lambda_\txL(T) = \lambda_\txL(0) \frac{1}{\sqrt{1- \left(\frac{T}{T_\txc}\right)^4}}}
\end{formula} \end{formula}
@ -97,8 +133,14 @@
\eng{ \eng{
\TODO{TODO} \TODO{TODO}
} }
\end{ttext} \end{ttext}
\begin{formula}{boundary_energy}
\desc{Boundary energy}{}{$\Delta E_\text{boundary}$ \TODO{TODO}}
\desc[german]{Grenzflächenenergie}{}{}
\eq{\Delta E_\text{boundary} = \Delta E_\text{con} - \Delta E_\txB = (\xi_\gl - \lambda) \frac{B_\text{c,th}^2}{2\mu_0}}
\end{formula}
\begin{formula}{coherence_length} \begin{formula}{coherence_length}
\desc{\GL Coherence Length}{}{} \desc{\GL Coherence Length}{}{}
\desc[german]{\GL Kohärenzlänge}{}{} \desc[german]{\GL Kohärenzlänge}{}{}
@ -111,20 +153,21 @@
\desc{\GL Penetration Depth / Field screening length}{}{} \desc{\GL Penetration Depth / Field screening length}{}{}
\desc[german]{\GL Eindringtiefe}{}{} \desc[german]{\GL Eindringtiefe}{}{}
\eq{ \eq{
\lambda_\gl &= \sqrt{\frac{m_\ssc\beta}{\mu_0 \abs{\alpha} q_s^2}} \\ \lambda_\gl &= \sqrt{\frac{m_\txs\beta}{\mu_0 \abs{\alpha} q_s^2}} \\
\lambda_\gl(T) &= \lambda_\gl(0) \frac{1}{\sqrt{1-\frac{T}{\Tcrit}}} \lambda_\gl(T) &= \lambda_\gl(0) \frac{1}{\sqrt{1-\frac{T}{\Tcrit}}}
} }
\end{formula} \end{formula}
\begin{formula}{first} \begin{formula}{first}
\desc{First Ginzburg-Landau Equation}{}{$\xi_\gl$ \fqEqRef{cm:sc:gl:coherence_length}, $\lambda_\gl$ \fqEqRef{cm:sc:gl:penetration_depth}} \desc{First Ginzburg-Landau Equation}{}{$\xi_\gl$ \fRef{cm:sc:gl:coherence_length}, $\lambda_\gl$ \fRef{cm:sc:gl:penetration_depth}}
\desc[german]{Erste Ginzburg-Landau Gleichung}{}{} \desc[german]{Erste Ginzburg-Landau Gleichung}{}{}
\eq{\alpha\Psi + \beta\abs{\Psi}^2 \Psi + \frac{1}{2m} (-i\hbar \Grad + 2e\vec{A})^2\Psi = 0} \eq{\alpha\Psi + \beta\abs{\Psi}^2 \Psi + \frac{1}{2m} (-i\hbar \Grad + 2e\vec{A})^2\Psi = 0}
\end{formula} \end{formula}
\begin{formula}{second} \begin{formula}{second}
\desc{Second Ginzburg-Landau Equation}{}{} \desc{Second Ginzburg-Landau Equation}{}{}
\desc[german]{Zweite Ginzburg-Landau Gleichung}{}{} \desc[german]{Zweite Ginzburg-Landau Gleichung}{}{}
\eq{\vec{j_\ssc} = \frac{ie\hbar}{m}(\Psi^*\Grad\Psi - \Psi\Grad\Psi^*) - \frac{4e^2}{m}\abs{\Psi}^2 \vec{A}} \eq{\vec{j_\txs} = \frac{ie\hbar}{m}(\Psi^*\Grad\Psi - \Psi\Grad\Psi^*) - \frac{4e^2}{m}\abs{\Psi}^2 \vec{A}}
\end{formula} \end{formula}
\TODO{proximity effect} \TODO{proximity effect}
@ -184,7 +227,7 @@
\end{formula} \end{formula}
\begin{formula}{bogoliubov-valatin} \begin{formula}{bogoliubov-valatin}
\desc{Bogoliubov-Valatin transformation}{Diagonalization of the \fqEqRef{cm:sc:micro:bcs:hamiltonian} to derive excitation energies}{} \desc{Bogoliubov-Valatin transformation}{Diagonalization of the \fRef{cm:sc:micro:bcs:hamiltonian} to derive excitation energies}{}
\desc[german]{Bogoliubov-Valatin transformation}{}{} \desc[german]{Bogoliubov-Valatin transformation}{}{}
\eq{ \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] \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]
@ -196,3 +239,10 @@
\desc[german]{}{}{} \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)} \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} \end{formula}
\begin{formula}{tcrit_temp}
\desc{Temperatur dependance of the crictial temperature}{}{}
\desc[german]{Temperaturabhängigkeit der kritischen Temperatur}{}{}
\eq{ \Bcth(T) = \Bcth(0) \left[1- \left(\frac{t}{T_\txc}\right) \right] }
\TODO{empirical relation, relate to BCS}
\end{formula}

9
src/cm/misc.tex
View File

@ -84,6 +84,15 @@
\ger{\GT{misc}} \ger{\GT{misc}}
]{misc} ]{misc}
\begin{formula}{vdw_material}
\desc{Van-der-Waals material}{2D materials}{}
\desc[german]{Van-der-Waals Material}{2D Materialien}{}
\ttxt{\eng{
Materials consiting of multiple 2D-layers held together by Van-der-Waals forces.
}\ger{
Aus mehreren 2D-Schichten bestehende Materialien, die durch Van-der-Waals Kräfte zusammengehalten werden.
}}
\end{formula}
\begin{formula}{work_function} \begin{formula}{work_function}

6
src/cm/semiconductors.tex
View File

@ -3,7 +3,7 @@
\ger{Halbleiter} \ger{Halbleiter}
]{semic} ]{semic}
\begin{formula}{types} \begin{formula}{types}
\desc{Intrinsic/extrinsic}{}{$n,p$ \fqEqRef{cm:semic:charge_density_eq}} \desc{Intrinsic/extrinsic}{}{$n,p$ \fRef{cm:semic:charge_density_eq}}
\desc[german]{Intrinsisch/Extrinsisch}{}{} \desc[german]{Intrinsisch/Extrinsisch}{}{}
\ttxt{ \ttxt{
\eng{ \eng{
@ -89,7 +89,7 @@
\end{formula} \end{formula}
\begin{bigformula}{schottky_barrier} \begin{bigformula}{schottky_barrier}
\desc{Schottky barrier}{Rectifying \fqEqRef{cm:sc:junctions:metal-sc}}{} \desc{Schottky barrier}{Rectifying \fRef{cm:sc:junctions:metal-sc}}{}
% \desc[german]{}{}{} % \desc[german]{}{}{}
\centering \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_separate.tex}}
@ -145,7 +145,7 @@
\eng[free_X]{for free Excitons} \eng[free_X]{for free Excitons}
\ger[free_X]{für freie Exzitons} \ger[free_X]{für freie Exzitons}
\begin{formula}{rydberg} \begin{formula}{rydberg}
\desc{Exciton Rydberg energy}{\gt{free_X}}{$R_\txH$ \fqEqRef{qm:h:rydberg_energy}} \desc{Exciton Rydberg energy}{\gt{free_X}}{$R_\txH$ \fRef{qm:h:rydberg_energy}}
\desc[german]{}{}{} \desc[german]{}{}{}
\eq{ \eq{
E(n) = - \left(\frac{\mu}{m_0\epsilon_r^2}\right) R_\txH \frac{1}{n^2} E(n) = - \left(\frac{\mu}{m_0\epsilon_r^2}\right) R_\txH \frac{1}{n^2}

16
src/cm/techniques.tex
View File

@ -21,12 +21,12 @@
\desc[german]{Raman-Spektroskopie}{}{} \desc[german]{Raman-Spektroskopie}{}{}
\begin{minipagetable}{raman} \begin{minipagetable}{raman}
\tentry{application}{ \tentry{application}{
\eng{Vibrational modes, Crystal structure, Doping, Band Gaps, Layer thickness in \fqEqRef{cm:misc:vdw_material}} \eng{Vibrational modes, Crystal structure, Doping, Band Gaps, Layer thickness in \fRef{cm:misc:vdw_material}}
\ger{Vibrationsmoden, Kristallstruktur, Dotierung, Bandlücke, Schichtdicke im \fqEqRef{cm:misc:vdw_material}} \ger{Vibrationsmoden, Kristallstruktur, Dotierung, Bandlücke, Schichtdicke im \fRef{cm:misc:vdw_material}}
} }
\tentry{how}{ \tentry{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})} \eng{Monochromatic light (\fRef{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}) } \ger{Monochromatisches Licht (\fRef{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} \end{minipagetable}
\begin{minipage}{0.45\textwidth} \begin{minipage}{0.45\textwidth}
@ -44,12 +44,12 @@
\desc[german]{Photolumeszenz-Spektroskopie}{}{} \desc[german]{Photolumeszenz-Spektroskopie}{}{}
\begin{minipagetable}{pl} \begin{minipagetable}{pl}
\tentry{application}{ \tentry{application}{
\eng{Crystal structure, Doping, Band Gaps, Layer thickness in \fqEqRef{cm:misc:vdw_material}} \eng{Crystal structure, Doping, Band Gaps, Layer thickness in \fRef{cm:misc:vdw_material}}
\ger{Kristallstruktur, Dotierung, Bandlücke, Schichtdicke im \fqEqRef{cm:misc:vdw_material}} \ger{Kristallstruktur, Dotierung, Bandlücke, Schichtdicke im \fRef{cm:misc:vdw_material}}
} }
\tentry{how}{ \tentry{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} \eng{Monochromatic light (\fRef{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} \ger{Monochromatisches Licht (\fRef{Laser}) bestrahlt Probe, Elektronen werden angeregt und relaxieren in das Leitungsband-Minimum und schließlich über die Bandlücke unter Photonemission}
} }
\end{minipagetable} \end{minipagetable}
\begin{minipage}{0.45\textwidth} \begin{minipage}{0.45\textwidth}

46
src/comp/ad.tex
View File

@ -3,12 +3,12 @@
% \ger{} % \ger{}
]{ad} ]{ad}
\begin{formula}{hamiltonian} \begin{formula}{hamiltonian}
\desc{Electron Hamiltonian}{}{$\hat{T}$ \fqEqRef{comp:est:kinetic_energy}, $\hat{V}$ \fqEqRef{comp:est:potential_energy}, $\txe$ \GT{electrons}, $\txn$ \GT{nucleons}} \desc{Electron Hamiltonian}{}{$\hat{T}$ \fRef{comp:est:kinetic_energy}, $\hat{V}$ \fRef{comp:est:potential_energy}, $\txe$ \GT{electrons}, $\txn$ \GT{nucleons}}
\desc[german]{Hamiltonian der Elektronen}{}{} \desc[german]{Hamiltonian der Elektronen}{}{}
\eq{\hat{H}_\txe = \hat{T}_\txe + V_{\txe \leftrightarrow \txe} + V_{\txn \leftrightarrow \txe}} \eq{\hat{H}_\txe = \hat{T}_\txe + V_{\txe \leftrightarrow \txe} + V_{\txn \leftrightarrow \txe}}
\end{formula} \end{formula}
\begin{formula}{ansatz} \begin{formula}{ansatz}
\desc{Wave function ansatz}{}{$\psi_\text{en}^n$ eigenstate $n$ of \fqEqRef{comp:est:hamiltonian}, $\psi_\txe^i$ eigenstate $i$ of \fqEqRef{comp:ad:bo:hamiltonian}, $\vecr,\vecR$ electron/nucleus positions, $\sigma$ electron spin, $c^{ni}$ coefficients} \desc{Wave function ansatz}{}{$\psi_\text{en}^n$ eigenstate $n$ of \fRef{comp:est:hamiltonian}, $\psi_\txe^i$ eigenstate $i$ of \fRef{comp:ad:hamiltonian}, $\vecr,\vecR$ electron/nucleus positions, $\sigma$ electron spin, $c^{ni}$ coefficients}
\desc[german]{Wellenfunktion Ansatz}{}{} \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)} \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} \end{formula}
@ -34,30 +34,30 @@
\ger{Born-Oppenheimer Näherung} \ger{Born-Oppenheimer Näherung}
]{bo} ]{bo}
\begin{formula}{adiabatic_approx} \begin{formula}{adiabatic_approx}
\desc{Adiabatic approximation}{Electronic configuration remains the same when atoms move (\absRef{adiabatic_theorem})}{$\Lambda_{ij}$ \fqEqRef{comp:ad:coupling_operator}} \desc{Adiabatic approximation}{Electronic configuration remains the same when atoms move (\absRef{adiabatic_theorem})}{$\Lambda_{ij}$ \fRef{comp:ad:coupling_operator}}
\desc[german]{Adiabatische Näherung}{Elektronenkonfiguration bleibt gleich bei Bewegung der Atome gleichl (\absRef{adiabatic_theorem})}{} \desc[german]{Adiabatische Näherung}{Elektronenkonfiguration bleibt gleich bei Bewegung der Atome gleichl (\absRef{adiabatic_theorem})}{}
\eq{\Lambda_{ij} = 0 \quad \text{\GT{for} } i\neq j} \eq{\Lambda_{ij} = 0 \quad \text{\GT{for} } i\neq j}
\end{formula} \end{formula}
\begin{formula}{approx} \begin{formula}{approx}
\desc{Born-Oppenheimer approximation}{Electrons are not influenced by the movement of the atoms}{\GT{see} \fqEqRef{comp:ad:equation}, $V_{\txn \leftrightarrow \txn} = \const$ absorbed into $E_\txe^j$} \desc{Born-Oppenheimer approximation}{Electrons are not influenced by the movement of the atoms}{\GT{see} \fRef{comp:ad:equation}, $V_{\txn \leftrightarrow \txn} = \const$ absorbed into $E_\txe^j$}
\desc[german]{Born-Oppenheimer Näherung}{Elektronen werden nicht durch die Bewegung der Atome beeinflusst}{} \desc[german]{Born-Oppenheimer Näherung}{Elektronen werden nicht durch die Bewegung der Atome beeinflusst}{}
\begin{gather} \begin{gather}
\Lambda_{ij} = 0 \Lambda_{ij} = 0
\shortintertext{\fqEqRef{comp:ad:bo:equation} \Rightarrow} % \shortintertext{\fRef{comp:ad:bo:equation} \Rightarrow}
\left[E_e^i\big(\{\vecR\}\big) + \hat{T}_\txn - E^n\right]c^{ni}\big(\{\vecR\}\big) = 0 \left[E_e^i\big(\{\vecR\}\big) + \hat{T}_\txn - E^n\right]c^{ni}\big(\{\vecR\}\big) = 0
\end{gather} \end{gather}
\end{formula} \end{formula}
\begin{formula}{surface} \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{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 \fRef{comp:ad: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}} \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 \fRef{comp:ad:hamiltonian}}
\begin{gather} \begin{gather}
V_\text{BO}\big(\{\vecR\}\big) = E_\txe^0\big(\{\vecR\}\big) \\ 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) M_I \ddot{\vecR}_I(t) = - \Grad_{\vecR_I} V_\text{BO}\big(\{\vecR(t)\}\big)
\end{gather} \end{gather}
\end{formula} \end{formula}
\begin{formula}{ansatz} \begin{formula}{ansatz}
\desc{Ansatz for \secEqRef{approx}}{Product of single electronic and single nuclear state}{} \desc{Ansatz for \fRef{::approx}}{Product of single electronic and single nuclear state}{}
\desc[german]{Ansatz für \secEqRef{approx}}{Produkt aus einem einzelnen elektronischen Zustand und einem Nukleus-Zustand}{} \desc[german]{Ansatz für \fRef{::approx}}{Produkt aus einem einzelnen elektronischen Zustand und einem Nukleus-Zustand}{}
\eq{ \eq{
\psi_\text{BO} = c^{n0} \big(\{\vecR\}\big) \,\psi_\txe^0 \big(\{\vecr,\sigma\},\{\vecR\}\big) \psi_\text{BO} = c^{n0} \big(\{\vecR\}\big) \,\psi_\txe^0 \big(\{\vecr,\sigma\},\{\vecR\}\big)
} }
@ -88,10 +88,14 @@
\begin{formula}{forces} \begin{formula}{forces}
\desc{Forces}{}{} \desc{Forces}{}{}
\desc[german]{Kräfte}{}{} \desc[german]{Kräfte}{}{}
\eq{\vec{F}_I = -\Grad_{\vecR_I} E \explOverEq{\fqEqRef{qm:se:hellmann_feynmann}} -\Braket{\psi(\vecR_I) | \left(\Grad_{\vecR_I} \hat{H}(\vecR_I)\right) | \psi(\vecR) }} \eq{
\vec{F}_I = -\Grad_{\vecR_I} E
\explOverEq{\fRef{qm:se:hellmann_feynmann}}
-\Braket{\psi(\vecR_I) | \left(\Grad_{\vecR_I} \hat{H}(\vecR_I)\right) | \psi(\vecR)}
}
\end{formula} \end{formula}
\begin{formula}{ionic_cycle} \begin{formula}{ionic_cycle}
\desc{Ionic cycle}{\fqEqRef{comp:est:dft:ks:scf} for geometry optimization}{} \desc{Ionic cycle}{\fRef{comp:est:dft:ks:scf} for geometry optimization}{}
\desc[german]{}{}{} \desc[german]{}{}{}
\ttxt{ \ttxt{
\eng{ \eng{
@ -99,11 +103,11 @@
\item Initial guess for $n(\vecr)$ \item Initial guess for $n(\vecr)$
\begin{enumerate} \begin{enumerate}
\item Calculate effective potential $V_\text{eff}$ \item Calculate effective potential $V_\text{eff}$
\item Solve \fqEqRef{comp:est:dft:ks:equation} \item Solve \fRef{comp:est:dft:ks:equation}
\item Calculate density $n(\vecr)$ \item Calculate density $n(\vecr)$
\item Repeat b-d until self consistent \item Repeat b-d until self consistent
\end{enumerate} \end{enumerate}
\item Calculate \secEqRef{forces} \item Calculate \fRef{:::forces}
\item If $F\neq0$, get new geometry by interpolating $R$ and restart \item If $F\neq0$, get new geometry by interpolating $R$ and restart
\end{enumerate} \end{enumerate}
} }
@ -146,8 +150,8 @@
\end{formula} \end{formula}
\begin{formula}{harmonic_approx} \begin{formula}{harmonic_approx}
\desc{Harmonic approximation}{Hessian matrix, 2nd order Taylor expansion of the \fqEqRef{comp:ad:bo:surface} around every nucleus position $\vecR_I^0$}{$\Phi_{IJ}^{\mu\nu}$ \secEqRef{force_constant_matrix}, $s$ displacement} \desc{Harmonic approximation}{Hessian matrix, 2nd order Taylor expansion of the \fRef{comp:ad:bo:surface} around every nucleus position $\vecR_I^0$}{$\Phi_{IJ}^{\mu\nu}$ \fRef{::force_constant_matrix}, $s$ displacement}
\desc[german]{Harmonische Näherung}{Hesse matrix, Taylor Entwicklung der \fqEqRef{comp:ad:bo:surface} in zweiter Oddnung um Atomposition $\vecR_I^0$}{} \desc[german]{Harmonische Näherung}{Hesse matrix, Taylor Entwicklung der \fRef{comp:ad:bo:surface} in zweiter Oddnung um Atomposition $\vecR_I^0$}{}
\eq{ V^\text{BO}(\{\vecR_I\}) \approx V^\text{BO}(\{\vecR_I^0\}) + \frac{1}{2} \sum_{I,J}^N \sum_{\mu,\nu}^3 s_I^\mu s_J^\nu \Phi_{IJ}^{\mu\nu} } \eq{ V^\text{BO}(\{\vecR_I\}) \approx V^\text{BO}(\{\vecR_I^0\}) + \frac{1}{2} \sum_{I,J}^N \sum_{\mu,\nu}^3 s_I^\mu s_J^\nu \Phi_{IJ}^{\mu\nu} }
\end{formula} \end{formula}
@ -166,13 +170,13 @@
\eq{\Phi_{IJ}^{\mu\nu} \approx \frac{\vecF_I^\mu(\vecR_1^0, \dots, \vecR_J^0+\Delta s_J^\nu,\dots, \vecR_N^0)}{\Delta s_J^\nu}} \eq{\Phi_{IJ}^{\mu\nu} \approx \frac{\vecF_I^\mu(\vecR_1^0, \dots, \vecR_J^0+\Delta s_J^\nu,\dots, \vecR_N^0)}{\Delta s_J^\nu}}
\end{formula} \end{formula}
\begin{formula}{dynamical_matrix} \begin{formula}{dynamical_matrix}
\desc{Dynamical matrix}{Mass reduced \absRef[fourier transform]{fourier_transform} of the \fqEqRef{comp:ad:latvib:force_constant_matrix}}{$\vec{L}$ vector from origin to unit cell $n$, $\alpha/\beta$ atom index in th unit cell, $\vecq$ \qtyRef{wave_vector}, $\Phi$ \fqEqRef{comp:ad:latvib:force_constant_matrix}, $M$ \qtyRef{mass}} \desc{Dynamical matrix}{Mass reduced \absRef[fourier transform]{fourier_transform} of the \fRef{comp:ad:latvib:force_constant_matrix}}{$\vec{L}$ vector from origin to unit cell $n$, $\alpha/\beta$ atom index in th unit cell, $\vecq$ \qtyRef{wave_vector}, $\Phi$ \fRef{comp:ad:latvib:force_constant_matrix}, $M$ \qtyRef{mass}}
% \desc[german]{}{}{} % \desc[german]{}{}{}
\eq{D_{\alpha\beta}^{\mu\nu} = \frac{1}{\sqrt{M_\alpha M_\beta}} \sum_{n^\prime} \Phi_{\alpha\beta}^{\mu\nu}(n-n^\prime) \e^{\I \vec{q}(\vec{L}_n - \vec{L}_{n^\prime})}} \eq{D_{\alpha\beta}^{\mu\nu} = \frac{1}{\sqrt{M_\alpha M_\beta}} \sum_{n^\prime} \Phi_{\alpha\beta}^{\mu\nu}(n-n^\prime) \e^{\I \vec{q}(\vec{L}_n - \vec{L}_{n^\prime})}}
\end{formula} \end{formula}
\begin{formula}{eigenvalue_equation} \begin{formula}{eigenvalue_equation}
\desc{Eigenvalue equation}{For a periodic crystal, reduces number of equations from $3N_p\times N$ to $3N_p$. Eigenvalues represent phonon band structure.}{$N_p$ number of atoms per unit cell, $\vecc$ displacement amplitudes, $\vecq$ \qtyRef{wave_vector}, $\mat{D}$ \secEqRef{dynamical_matrix}} \desc{Eigenvalue equation}{For a periodic crystal, reduces number of equations from $3N_p\times N$ to $3N_p$. Eigenvalues represent phonon band structure.}{$N_p$ number of atoms per unit cell, $\vecc$ displacement amplitudes, $\vecq$ \qtyRef{wave_vector}, $\mat{D}$ \fRef{::dynamical_matrix}}
\desc[german]{Eigenwertgleichung}{}{} \desc[german]{Eigenwertgleichung}{}{}
\eq{\omega^2 \vecc(\vecq) = \mat{D}(\vecq) \vecc(\vecq) } \eq{\omega^2 \vecc(\vecq) = \mat{D}(\vecq) \vecc(\vecq) }
\end{formula} \end{formula}
@ -186,7 +190,7 @@
\desc{Quasi-harmonic approximation}{}{} \desc{Quasi-harmonic approximation}{}{}
\desc[german]{}{}{} \desc[german]{}{}{}
\ttxt{\eng{ \ttxt{\eng{
Include thermal expansion by assuming \fqEqRef{comp:ad:bo:surface} is volume dependant. Include thermal expansion by assuming \fRef{comp:ad:bo:surface} is volume dependant.
}} }}
\end{formula} \end{formula}
@ -194,7 +198,7 @@
\desc{Pertubative approaches}{}{} \desc{Pertubative approaches}{}{}
% \desc[german]{Störungs}{}{} % \desc[german]{Störungs}{}{}
\ttxt{\eng{ \ttxt{\eng{
Expand \fqEqRef{comp:ad:latvib:force_constant_matrix} to third order. Expand \fRef{comp:ad:latvib:force_constant_matrix} to third order.
}} }}
\end{formula} \end{formula}
@ -244,7 +248,7 @@
\ttxt{\eng{ \ttxt{\eng{
\begin{enumerate} \begin{enumerate}
\item Calculate electronic ground state of current nucleui configuration $\{\vecR(t)\}$ with \abbrRef{ksdft} \item Calculate electronic ground state of current nucleui configuration $\{\vecR(t)\}$ with \abbrRef{ksdft}
\item \hyperref[f:comp:ad:opt:forces]{Calculate forces} from the \fqEqRef{comp:ad:bo:surface} \item \fRef[Calculate forces]{comp:ad:opt:forces} from the \fRef{comp:ad:bo:surface}
\item Update positions and velocities \item Update positions and velocities
\end{enumerate} \end{enumerate}
\begin{itemize} \begin{itemize}
@ -375,7 +379,7 @@
\end{formula} \end{formula}
\begin{formula}{vdos} \abbrLabel{VDOS} \begin{formula}{vdos} \abbrLabel{VDOS}
\desc{Vibrational density of states (VDOS)}{}{$S_{v_i}$ velocity \secEqRef{spectral_density} of particle $I$} \desc{Vibrational density of states (VDOS)}{}{$S_{v_i}$ velocity \fRef{::spectral_density} of particle $I$}
\desc[german]{Vibrationszustandsdicht (VDOS)}{}{} \desc[german]{Vibrationszustandsdicht (VDOS)}{}{}
\eq{g(\omega) \sim \sum_{I=1}^N M_I S_{v_I}(\omega)} \eq{g(\omega) \sim \sum_{I=1}^N M_I S_{v_I}(\omega)}
\end{formula} \end{formula}

26
src/comp/est.tex
View File

@ -14,7 +14,7 @@
\eq{\hat{V}_{i \leftrightarrow j} &= -\sum_{k,l} \frac{Z_i Z_j e^2}{\abs{\vecr_k - \vecr_l}}} \eq{\hat{V}_{i \leftrightarrow j} &= -\sum_{k,l} \frac{Z_i Z_j e^2}{\abs{\vecr_k - \vecr_l}}}
\end{formula} \end{formula}
\begin{formula}{hamiltonian} \begin{formula}{hamiltonian}
\desc{Electronic structure Hamiltonian}{}{$\hat{T}$ \fqEqRef{comp:est:kinetic_energy}, $\hat{V}$ \fqEqRef{comp:est:potential_energy}, $\txe$ \GT{electrons}, $\txn$ \GT{nucleons}} \desc{Electronic structure Hamiltonian}{}{$\hat{T}$ \fRef{comp:est:kinetic_energy}, $\hat{V}$ \fRef{comp:est: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}} \eq{\hat{H} &= \hat{T}_\txe + \hat{T}_\txn + V_{\txe \leftrightarrow \txe} + V_{\txn \leftrightarrow \txe} + V_{\txn \leftrightarrow \txn}}
\end{formula} \end{formula}
\begin{formula}{mean_field} \begin{formula}{mean_field}
@ -64,8 +64,8 @@
\begin{ttext} \begin{ttext}
\eng{ \eng{
\begin{itemize} \begin{itemize}
\item Assumes wave functions are \fqEqRef{qm:other:slater_det} \Rightarrow Approximation \item Assumes wave functions are \fRef{qm:other:slater_det} \Rightarrow Approximation
\item \fqEqRef{comp:est:mean_field} theory obeying the Pauli principle \item \fRef{comp:est:mean_field} theory obeying the Pauli principle
\item Self-interaction free: Self interaction is cancelled out by the Fock-term \item Self-interaction free: Self interaction is cancelled out by the Fock-term
\end{itemize} \end{itemize}
} }
@ -76,14 +76,14 @@
$\varphi_\xi$ single particle wavefunction of $\xi$th orbital, $\varphi_\xi$ single particle wavefunction of $\xi$th orbital,
$\hat{T}$ kinetic electron energy, $\hat{T}$ kinetic electron energy,
$\hat{V}_{\text{en}}$ electron-nucleus attraction, $\hat{V}_{\text{en}}$ electron-nucleus attraction,
$\hat{V}_{\text{HF}}$ \fqEqRef{comp:dft:hf:potential}, $h\hat{V}_{\text{HF}}$ \fRef{comp:est:dft:hf:potential},
$x = \vecr,\sigma$ position and spin $x = \vecr,\sigma$ position and spin
} }
\desc[german]{Hartree-Fock Gleichung}{}{ \desc[german]{Hartree-Fock Gleichung}{}{
$\varphi_\xi$ ein-Teilchen Wellenfunktion des $\xi$-ten Orbitals, $\varphi_\xi$ ein-Teilchen Wellenfunktion des $\xi$-ten Orbitals,
$\hat{T}$ kinetische Energie der Elektronen, $\hat{T}$ kinetische Energie der Elektronen,
$\hat{V}_{\text{en}}$ Electron-Kern Anziehung, $\hat{V}_{\text{en}}$ Electron-Kern Anziehung,
$\hat{V}_{\text{HF}}$ \fqEqRef{comp:dft:hf:potential}, $\hat{V}_{\text{HF}}$ \fRef{comp:est:dft:hf:potential},
$x = \vecr,\sigma$ Position and Spin $x = \vecr,\sigma$ Position and Spin
} }
\eq{ \eq{
@ -158,7 +158,7 @@
\eq{n(\vecr) = \sum_{i=1}^N \abs{\phi_i(\vecr)}^2} \eq{n(\vecr) = \sum_{i=1}^N \abs{\phi_i(\vecr)}^2}
\end{formula} \end{formula}
\begin{formula}{functional} \begin{formula}{functional}
\desc{Kohn-Sham functional}{}{$T_\text{KS}$ kinetic enery, $V_\text{ext}$ external potential, $E_\txH$ \hyperref[f:comp:est:dft:hf:potential]{Hartree term}, $E_\text{XC}$ \fqEqRef{comp:est:dft:xc:xc}} \desc{Kohn-Sham functional}{}{$T_\text{KS}$ kinetic enery, $V_\text{ext}$ external potential, $E_\txH$ \fRef[Hartree term]{comp:est:dft:hf:potential}, $E_\text{XC}$ \fRef{comp:est:dft:xc:xc}}
\desc[german]{Kohn-Sham Funktional}{}{} \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)] } \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} \end{formula}
@ -186,7 +186,7 @@
\begin{enumerate} \begin{enumerate}
\item Initial guess for $n(\vecr)$ \item Initial guess for $n(\vecr)$
\item Calculate effective potential $V_\text{eff}$ \item Calculate effective potential $V_\text{eff}$
\item Solve \fqEqRef{comp:est:dft:ks:equation} \item Solve \fRef{comp:est:dft:ks:equation}
\item Calculate density $n(\vecr)$ \item Calculate density $n(\vecr)$
\item Repeat 2-4 until self consistent \item Repeat 2-4 until self consistent
\end{enumerate} \end{enumerate}
@ -212,14 +212,14 @@
}} }}
\end{formula} \end{formula}
\begin{formula}{lda} \begin{formula}{lda}
\desc{Local density approximation (LDA)}{Simplest DFT functionals}{$\epsilon_\txX$ calculated exchange energy from \hyperref[f:comp:qmb:models:heg]{HEG model}, $\epsilon_\txC$ correlation energy calculated with \fqSecRef{comp:qmb:methods:qmonte-carlo}} \desc{Local density approximation (LDA)}{Simplest DFT functionals}{$\epsilon_\txX$ calculated exchange energy from \fRef[HEG model]{comp:qmb:models:heg}, $\epsilon_\txC$ correlation energy calculated with \fRef{comp:qmb:methods:qmonte-carlo}}
\desc[german]{}{}{} \desc[german]{}{}{}
\abbrLabel{LDA} \abbrLabel{LDA}
\eq{E_\text{XC}^\text{LDA}[n(\vecr)] = \int \d^3r\,n(r) \Big[\epsilon_\txX[n(\vecr)] + \epsilon_\txC[n(\vecr)]\Big]} \eq{E_\text{XC}^\text{LDA}[n(\vecr)] = \int \d^3r\,n(r) \Big[\epsilon_\txX[n(\vecr)] + \epsilon_\txC[n(\vecr)]\Big]}
\end{formula} \end{formula}
\begin{formula}{gga} \begin{formula}{gga}
\desc{Generalized gradient approximation (GGA)}{}{$\epsilon_\txX$ calculated exchange energy from \hyperref[f:comp:qmb:models:heg]{HEG model}, $F_\text{XC}$ function containing exchange-correlation energy dependency on $n$ and $\Grad n$} \desc{Generalized gradient approximation (GGA)}{}{$\epsilon_\txX$ calculated exchange energy from \fRef[HEG model]{comp:qmb:models:heg}, $F_\text{XC}$ function containing exchange-correlation energy dependency on $n$ and $\Grad n$}
\desc[german]{}{}{} \desc[german]{}{}{}
\abbrLabel{GGA} \abbrLabel{GGA}
\eq{E_\text{XC}^\text{GGA}[n(\vecr)] = \int \d^3r\,n(r) \epsilon_\txX[n(\vecr)]\,F_\text{XC}[n(\vecr), \Grad n(\vecr)]} \eq{E_\text{XC}^\text{GGA}[n(\vecr)] = \int \d^3r\,n(r) \epsilon_\txX[n(\vecr)]\,F_\text{XC}[n(\vecr), \Grad n(\vecr)]}
@ -232,7 +232,7 @@
\desc[german]{Hybride Funktionale}{}{$\alpha$ mixing paramter, $E_\txX$ exchange energy, $E_\txC$ correlation energy} \desc[german]{Hybride Funktionale}{}{$\alpha$ mixing paramter, $E_\txX$ exchange energy, $E_\txC$ correlation energy}
\eq{\alpha E_\txX^\text{HF} + (1-\alpha) E_\txX^\text{GGA} + E_\txC^\text{GGA}} \eq{\alpha E_\txX^\text{HF} + (1-\alpha) E_\txX^\text{GGA} + E_\txC^\text{GGA}}
\ttxt{\eng{ \ttxt{\eng{
Include \hyperref[f:comp:dft:hf:potential]{Fock term} (exact exchange) in other functional, like \abbrRef{gga}. Computationally expensive Include \fRef[Fock term]{comp:est:dft:hf:potential} (exact exchange) in other functional, like \abbrRef{gga}. Computationally expensive
}} }}
\end{formula} \end{formula}
@ -246,7 +246,7 @@
\end{gather} \end{gather}
\separateEntries \separateEntries
\ttxt{\eng{ \ttxt{\eng{
Use \abbrRef{gga} and \hyperref[comp:est:dft:hf:potential]{Fock} exchange for short ranges (SR) and only \abbrRef{GGA} for long ranges (LR). Use \abbrRef{gga} and \fRef[Fock]{comp:est:dft:hf:potential} exchange for short ranges (SR) and only \abbrRef{GGA} for long ranges (LR).
\abbrRef{GGA} correlation is always used. Useful when dielectric screening reduces long range interactions, saves computational cost. \abbrRef{GGA} correlation is always used. Useful when dielectric screening reduces long range interactions, saves computational cost.
}} }}
\end{formula} \end{formula}
@ -255,7 +255,7 @@
\desc{Comparison of DFT functionals}{}{} \desc{Comparison of DFT functionals}{}{}
\desc[german]{Vergleich von DFT Funktionalen}{}{} \desc[german]{Vergleich von DFT Funktionalen}{}{}
% \begin{tabular}{l|c} % \begin{tabular}{l|c}
% \hyperref[f:comp:est:dft:hf:potential]{Hartree-Fock} & only exchange, no correlation \Rightarrow upper bound of GS energy \\ % \fRef[Hartree-Fock]{comp:est:dft:hf:potential} & only exchange, no correlation \Rightarrow upper bound of GS energy \\
% \abbrRef{lda} & understimates e repulsion \Rightarrow Overbinding \\ % \abbrRef{lda} & understimates e repulsion \Rightarrow Overbinding \\
% \abbrRef{gga} & underestimate band gap \\ % \abbrRef{gga} & underestimate band gap \\
% hybrid & underestimate band gap % hybrid & underestimate band gap
@ -374,7 +374,7 @@
\ger{Basis-Sets} \ger{Basis-Sets}
]{basis} ]{basis}
\begin{formula}{plane_wave} \begin{formula}{plane_wave}
\desc{Plane wave basis}{Plane wave ansatz in \fqEqRef{comp:est:dft:ks:equation}\\Good for periodic structures, allows computation parallelization over a sample points in the \abbrRef{brillouin_zone}}{} \desc{Plane wave basis}{Plane wave ansatz in \fRef{comp:est:dft:ks:equation}\\Good for periodic structures, allows computation parallelization over a sample points in the \abbrRef{brillouin_zone}}{}
\desc[german]{Ebene Wellen als Basis}{}{} \desc[german]{Ebene Wellen als Basis}{}{}
\eq{\sum_{\vecG^\prime} \left[\frac{\hbar^2 \abs{\vecG+\veck}^2}{2m} \delta_{\vecG,\vecG^\prime} + V_\text{eff}(\vecG-\vecG^\prime)\right] c_{i,\veck,\vecG^\prime} = \epsilon_{i,\veck} c_{i,\veck,\vecG}} \eq{\sum_{\vecG^\prime} \left[\frac{\hbar^2 \abs{\vecG+\veck}^2}{2m} \delta_{\vecG,\vecG^\prime} + V_\text{eff}(\vecG-\vecG^\prime)\right] c_{i,\veck,\vecG^\prime} = \epsilon_{i,\veck} c_{i,\veck,\vecG}}
\end{formula} \end{formula}

42
src/comp/ml.tex
View File

@ -48,8 +48,8 @@
\ger{Lineare Regression} \ger{Lineare Regression}
]{linear} ]{linear}
\begin{formula}{eq} \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, $\vec{\beta}$ weights, $N$ samples, $M$ features, $L$ output variables} \desc{Linear regression}{Fits the data under the assumption of \fRef[normally distributed errors]{math:pt:distributions:cont:normal}}{$\mat{x}\in\R^{N\times M}$ input data, $\mat{y}\in\R^{N\times L}$ output data, $\mat{b}$ bias, $\vec{\beta}$ 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}}{} \desc[german]{Lineare Regression}{Fitted Daten unter der Annahme \fRef[normalverteilter Fehler]{math:pt:distributions:cont:normal}}{}
\eq{\mat{y} = \mat{\epsilon} + \mat{x} \cdot \vec{\beta}} \eq{\mat{y} = \mat{\epsilon} + \mat{x} \cdot \vec{\beta}}
\end{formula} \end{formula}
\begin{formula}{design_matrix} \begin{formula}{design_matrix}
@ -60,13 +60,13 @@
} }
\end{formula} \end{formula}
\begin{formula}{scalar_bias} \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}, $\vec{\beta}$ weights} \desc{Linear regression with scalar bias}{Using the design matrix, the scalar is absorbed into the weight vector}{$\mat{y}$ output data, $\mat{X}$ \fRef{::design_matrix}, $\vec{\beta}$ weights}
\desc[german]{Lineare Regression mit skalarem Bias}{Durch die Designmatrix wird der Bias in den Gewichtsvektor absorbiert}{} \desc[german]{Lineare Regression mit skalarem Bias}{Durch die Designmatrix wird der Bias in den Gewichtsvektor absorbiert}{}
\eq{\mat{y} = \mat{X} \cdot \vec{\beta}} \eq{\mat{y} = \mat{X} \cdot \vec{\beta}}
\end{formula} \end{formula}
\begin{formula}{normal_equation} \begin{formula}{normal_equation}
\desc{Normal equation}{Solves \fqEqRef{comp:ml:reg:linear:scalar_bias} with \fqEqRef{comp:ml:performance:mse}}{$\mat{y}$ output data, $\mat{X}$ \fqEqRef{comp:ml:reg:linear:design_matrix}, $\vec{\beta}$ weights} \desc{Normal equation}{Solves \fRef{comp:ml:reg:linear:scalar_bias} with \fRef{comp:ml:performance:mean_square_error}}{$\mat{y}$ output data, $\mat{X}$ \fRef{::design_matrix}, $\vec{\beta}$ weights}
\desc[german]{Normalengleichung}{Löst \fqEqRef{comp:ml:reg:linear:scalar_bias} mit \fqEqRef{comp:ml:performance:mse}}{} \desc[german]{Normalengleichung}{Löst \fRef{comp:ml:reg:linear:scalar_bias} mit \fRef{comp:ml:performance:mean_square_error}}{}
\eq{\vec{\beta} = \left(\mat{X}^\T \mat{X}\right)^{-1} \mat{X}^T \mat{y}} \eq{\vec{\beta} = \left(\mat{X}^\T \mat{X}\right)^{-1} \mat{X}^T \mat{y}}
\end{formula} \end{formula}
@ -112,7 +112,7 @@
\desc{Bayesian linear regression}{}{} \desc{Bayesian linear regression}{}{}
\desc[german]{Bayes'sche lineare Regression}{}{} \desc[german]{Bayes'sche lineare Regression}{}{}
\ttxt{\eng{ \ttxt{\eng{
Assume a \fqEqRef{math:pt:bayesian:prior} distribution over the weights. Assume a \fRef{math:pt:bayesian:prior} distribution over the weights.
Offers uncertainties in addition to the predictions. Offers uncertainties in addition to the predictions.
}} }}
\end{formula} \end{formula}
@ -123,16 +123,16 @@
\ttxt{\eng{ \ttxt{\eng{
Applies a L2 norm penalty on the weights. Applies a L2 norm penalty on the weights.
This ensures unimportant features are less regarded and do not encode noise. This ensures unimportant features are less regarded and do not encode noise.
\\Corresponds to assuming a \fqEqRef{math:pt:bayesian:prior} \absRef{multivariate_normal_distribution} with $\vec{\mu} = 0$ and independent components ($\mat{\Sigma}$) for the weights. \\Corresponds to assuming a \fRef{math:pt:bayesian:prior} \absRef{multivariate_normal_distribution} with $\vec{\mu} = 0$ and independent components ($\mat{\Sigma}$) for the weights.
}\ger{ }\ger{
Reduziert Gewichte mit der L2-Norm. Reduziert Gewichte mit der L2-Norm.
Dadurch werden unwichtige Features nicht berücksichtigt (kleines Gewicht) und enkodieren nicht Noise. Dadurch werden unwichtige Features nicht berücksichtigt (kleines Gewicht) und enkodieren nicht Noise.
\\Entspricht der Annahme einer \absRef[Normalverteilung]{multivariate_normal_distribution} mit $\vec{\mu}=0$ und unanhängingen Komponenten ($\mat{Sigma}$ diagonaol) der die Gewichte als \fqEqRef{math:pt:bayesian:prior}. \\Entspricht der Annahme einer \absRef[Normalverteilung]{multivariate_normal_distribution} mit $\vec{\mu}=0$ und unanhängingen Komponenten ($\mat{Sigma}$ diagonaol) der die Gewichte als \fRef{math:pt:bayesian:prior}.
}} }}
\end{formula} \end{formula}
\begin{formula}{ridge_weights} \begin{formula}{ridge_weights}
\desc{Optimal weights}{for ridge regression}{$\lambda = \frac{\sigma^2}{\xi^2}$ shrinkage parameter, $\xi$ \absRef{variance} of the gaussian \fqEqRef{math:pt:bayesian:prior}, $\sigma$ \absRef{variance} of the gaussian likelihood of the data} \desc{Optimal weights}{for ridge regression}{$\lambda = \frac{\sigma^2}{\xi^2}$ shrinkage parameter, $\xi$ \absRef{variance} of the gaussian \fRef{math:pt:bayesian:prior}, $\sigma$ \absRef{variance} of the gaussian likelihood of the data}
\desc[german]{Optimale Gewichte}{für Ridge Regression}{} \desc[german]{Optimale Gewichte}{für Ridge Regression}{}
\eq{\vec{\beta} = \left(\mat{X}^\T \mat{X} + \lambda \mathcal{1} \right)^{-1} \mat{X}^\T \vecy} \eq{\vec{\beta} = \left(\mat{X}^\T \mat{X} + \lambda \mathcal{1} \right)^{-1} \mat{X}^\T \vecy}
\TODO{Does this only work for gaussian data?} \TODO{Does this only work for gaussian data?}
@ -143,11 +143,11 @@
\desc[german]{Lasso Regression}{}{} \desc[german]{Lasso Regression}{}{}
\ttxt{\eng{ \ttxt{\eng{
Applies a L1 norm penalty on the weights, which means features can be disregarded entirely. Applies a L1 norm penalty on the weights, which means features can be disregarded entirely.
\\Corresponds to assuming a \absRef{laplace_distribution} for the weights as \fqEqRef{math:pt:bayesian:prior}. \\Corresponds to assuming a \absRef{laplace_distribution} for the weights as \fRef{math:pt:bayesian:prior}.
}\ger{ }\ger{
Reduziert Gewichte mit der L1-Norm. Reduziert Gewichte mit der L1-Norm.
Unwichtige Features werden reduziert und können auch ganz vernachlässigt werden und enkodieren nicht Noise. Unwichtige Features werden reduziert und können auch ganz vernachlässigt werden und enkodieren nicht Noise.
\\Entspricht der Annahme einer \absRef[Laplace-Verteilung]{laplace_distribution} der die Gewichte als \fqEqRef{math:pt:bayesian:prior}. \\Entspricht der Annahme einer \absRef[Laplace-Verteilung]{laplace_distribution} der die Gewichte als \fRef{math:pt:bayesian:prior}.
}} }}
\end{formula} \end{formula}
@ -158,7 +158,7 @@
% \desc[german]{}{}{} % \desc[german]{}{}{}
\ttxt{\eng{ \ttxt{\eng{
Gaussian process: A distribtuion over functions that produce jointly gaussian distribution. Gaussian process: A distribtuion over functions that produce jointly gaussian distribution.
Multivariate normal distribution like \secEqRef{bayesian}, except that $\vec{\mu}$ and $\mat{\Sigma}$ are functions. Multivariate normal distribution like \fRef{:::linear_regression}, except that $\vec{\mu}$ and $\mat{\Sigma}$ are functions.
GPR: non-parametric Bayesion regressor, does not assume fixed functional form for the underlying data, instead, the data determines the functional shape, GPR: non-parametric Bayesion regressor, does not assume fixed functional form for the underlying data, instead, the data determines the functional shape,
with predictions governed by the covariance structure defined by the kernel (often \abbrRef{radial_basis_function}). with predictions governed by the covariance structure defined by the kernel (often \abbrRef{radial_basis_function}).
@ -168,7 +168,23 @@
\end{formula} \end{formula}
\TODO{soap} \begin{formula}{soap}
\desc{Smooth overlap of atomic atomic positions (SOAP)}{}{}
% \desc[german]{}{}{}
\ttxt{\eng{
Goal: symmetric invariance, smoothness, completeness (completeness not achieved)
\\Gaussian smeared density expanded in \abbrRef{radial_basis_function} and spherical harmonics.
}}
\end{formula}
\begin{formula}{gaussian_approximation_potential}
\desc{Gaussian approximation potential}{Bond-order potential}{$V_\text{rep/attr}$ repulsive / attractive potential}
% \desc[german]{}{}{}
\ttxt{\eng{
Models atomic interactions via a \textit{bond-order} term $b$.
}}
\eq{V_\text{BondOrder}(\vecR_M, \vecR_N) = V_\text{rep}(\vecR_M, \vecR_N) + b_{MNK} V_\text{attr}(\vecR_M, \vecR_N)}
\end{formula}
\Subsection[ \Subsection[
\eng{Gradient descent} \eng{Gradient descent}

9
src/constants.tex
View File

@ -53,6 +53,15 @@
} }
\end{formula} \end{formula}
\begin{formula}{flux_quantum}
\desc{Flux quantum}{}{}
\desc[german]{Flussquantum}{}{}
\constant{\Phi_0}{def}{
\val{2.067 833 848 \xE{-15}}{\weber=\volt\s=\kg\m^2\per\s^2\ampere}
}
\eq{\Phi_0 = \frac{h}{2e}}
\end{formula}
\begin{formula}{atomic_mass_unit} \begin{formula}{atomic_mass_unit}
\desc{Atomic mass unit}{}{} \desc{Atomic mass unit}{}{}
\desc[german]{Atomare Massneinheit}{}{} \desc[german]{Atomare Massneinheit}{}{}

2
src/ed/el.tex
View File

@ -45,7 +45,7 @@
\end{formula} \end{formula}
\begin{formula}{electric_susceptibility} \begin{formula}{electric_susceptibility}
\desc{Electric susceptibility}{Describes how polarized a dielectric material becomes when an electric field is applied}{$\epsilon_\txr$ \fqEqRef{ed:el:relative_permittivity}} \desc{Electric susceptibility}{Describes how polarized a dielectric material becomes when an electric field is applied}{$\epsilon_\txr$ \fRef{ed:el:relative_permittivity}}
\desc[german]{Elektrische Suszeptibilität}{Beschreibt wie stark ein dielektrisches Material polarisiert wird, wenn ein elektrisches Feld angelegt wird}{} \desc[german]{Elektrische Suszeptibilität}{Beschreibt wie stark ein dielektrisches Material polarisiert wird, wenn ein elektrisches Feld angelegt wird}{}
\quantity{\chi_\txe}{}{s} \quantity{\chi_\txe}{}{s}
\eq{ \eq{

4
src/ed/em.tex
View File

@ -37,8 +37,8 @@
\end{formula} \end{formula}
\begin{formula}{hamiltonian} \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{Hamiltonian of a particle in an electromagnetic field}{In the \fRef{ed:em:gauge:coulomb}}{\QtyRef{mass}, $\hat{p}$ \fRef{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}}{} \desc[german]{Hamiltonian eines Teilchens im elektromagnetischen Feld}{In der \fRef{ed:em:gauge:coulomb}}{}
\eq{ \eq{
\hat{H} = \frac{1}{2m} \left[\hat{p} \ \frac{e \vec{A}}{c}\right]^2 \hat{H} = \frac{1}{2m} \left[\hat{p} \ \frac{e \vec{A}}{c}\right]^2
} }

12
src/ed/mag.tex
View File

@ -11,8 +11,8 @@
\end{formula} \end{formula}
\begin{formula}{magnetic_flux_density} \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{Magnetic flux density}{Defined by \fRef{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}}{} \desc[german]{Magnetische Flussdichte}{Definiert über \fRef{ed:mag:lorentz}}{}
\quantity{\vec{B}}{\tesla=\volt\s\per\m^2=\newton\per\ampere\m=\kg\per\ampere\s^2}{} \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})} \eq{\vec{B} = \mu_0 (\vec{H}+\vec{M})}
\end{formula} \end{formula}
@ -88,7 +88,7 @@
\end{formula} \end{formula}
\begin{formula}{magnetic_susceptibility} \begin{formula}{magnetic_susceptibility}
\desc{Susceptibility}{}{$\mu_\txr$ \fqEqRef{ed:mag:relative_permeability}} \desc{Susceptibility}{}{$\mu_\txr$ \fRef{ed:mag:relative_permeability}}
\desc[german]{Suszeptibilität}{}{} \desc[german]{Suszeptibilität}{}{}
\eq{\chi_\txm = \pdv{M}{B} = \mu_\txr - 1} \eq{\chi_\txm = \pdv{M}{B} = \mu_\txr - 1}
\end{formula} \end{formula}
@ -101,19 +101,19 @@
\ger{Magnetische Materialien} \ger{Magnetische Materialien}
]{materials} ]{materials}
\begin{formula}{paramagnetism} \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{Paramagnetism}{Magnetic field strengthend in the material}{$\mu$ \fRef{ed:mag:magnetic_permeability}, $\chi_\txm$ \fRef{ed:mag:magnetic_susceptibility}}
\desc[german]{Paramagnetismus}{Magnetisches Feld wird im Material verstärkt}{} \desc[german]{Paramagnetismus}{Magnetisches Feld wird im Material verstärkt}{}
\eq{\mu_\txr &> 1 \\ \chi_\txm &> 0} \eq{\mu_\txr &> 1 \\ \chi_\txm &> 0}
\end{formula} \end{formula}
\begin{formula}{diamagnetism} \begin{formula}{diamagnetism}
\desc{Diamagnetism}{Magnetic field expelled from material}{$\mu$ \fqEqRef{ed:mag:magnetic_permeability}, $\chi_\txm$ \fqEqRef{ed:mag:magnetic_susceptibility}} \desc{Diamagnetism}{Magnetic field expelled from material}{$\mu$ \fRef{ed:mag:magnetic_permeability}, $\chi_\txm$ \fRef{ed:mag:magnetic_susceptibility}}
\desc[german]{Diamagnetismus}{Magnetisches Feld wird aus dem Material gedrängt}{} \desc[german]{Diamagnetismus}{Magnetisches Feld wird aus dem Material gedrängt}{}
\eq{0 < \mu_\txr < 1 \\ -1 < \chi_\txm < 0} \eq{0 < \mu_\txr < 1 \\ -1 < \chi_\txm < 0}
\end{formula} \end{formula}
\begin{formula}{ferromagnetism} \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{Ferromagnetism}{Magnetic moments align to external magnetic field and stay aligned when the field is turned off (Remanescence)}{$\mu$ \fRef{ed:mag:magnetic_permeability}, $\chi_\txm$ \fRef{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)}{} \desc[german]{Ferromagnetismus}{Magnetische Momente werden am äußeren Feld ausgerichtet und behalten diese ausrichtung auch wenn das Feld abgeschaltet wird (Remanenz)}{}
\eq{ \eq{
\mu_\txr \gg 1 \mu_\txr \gg 1

2
src/ed/optics.tex
View File

@ -79,7 +79,7 @@
\begin{formula}{intensity} \begin{formula}{intensity}
\desc{Electromagnetic radiation intensity}{Surface power density}{$S$ \fqEqRef{ed:poynting}} \desc{Electromagnetic radiation intensity}{Surface power density}{$S$ \fRef{ed:poynting}}
\desc[german]{Elektromagnetische Strahlungsintensität}{Flächenleistungsdichte}{} \desc[german]{Elektromagnetische Strahlungsintensität}{Flächenleistungsdichte}{}
\quantity{I}{\watt\per\m^2=\k\per\s^3}{s} \quantity{I}{\watt\per\m^2=\k\per\s^3}{s}
\eq{I = \abs{\braket{S}_t}} \eq{I = \abs{\braket{S}_t}}

26
src/main.tex
View File

@ -20,7 +20,7 @@
% FORMATING % FORMATING
\usepackage{float} % float barrier \usepackage{float} % float barrier
\usepackage{subcaption} % subfigures \usepackage{subcaption} % subfigures
\usepackage[hidelinks]{hyperref} % hyperrefs for \fqEqRef, \qtyRef, etc \usepackage[hidelinks]{hyperref} % hyperrefs for \fRef, \qtyRef, etc
\usepackage[shortlabels]{enumitem} % easily change enum symbols to i), a. etc \usepackage[shortlabels]{enumitem} % easily change enum symbols to i), a. etc
\setlist{noitemsep} % no vertical space between items \setlist{noitemsep} % no vertical space between items
\setlist[1]{labelindent=\parindent} % < Usually a good idea \setlist[1]{labelindent=\parindent} % < Usually a good idea
@ -87,30 +87,24 @@
\newcommand{\TODO}[1]{{\color{fg-red}TODO:#1}} \newcommand{\TODO}[1]{{\color{fg-red}TODO:#1}}
\newcommand{\ts}{\textsuperscript} \newcommand{\ts}{\textsuperscript}
% 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{circuit.tex}
\input{util/macros.tex} \input{util/macros.tex}
\input{util/math-macros.tex} \input{util/math-macros.tex}
\input{util/environments.tex} % requires util/translation.tex to be loaded first \input{util/environments.tex} % requires util/translation.tex to be loaded first
\usepackage{pkg/mqlua} \usepackage{mqlua}
\usepackage{pkg/mqfqname} \usepackage{mqfqname}
\usepackage{mqref}
% TRANSLATION % TRANSLATION
% \usepackage{translations} % \usepackage{translations}
\usepackage{pkg/mqtranslation} \usepackage{mqtranslation}
\input{util/colorscheme.tex} \input{util/colorscheme.tex}
\input{util/colors.tex} % after colorscheme \input{util/colors.tex} % after colorscheme
\usepackage{pkg/mqconstant} \usepackage{mqconstant}
\usepackage{pkg/mqquantity} \usepackage{mqquantity}
\usepackage{pkg/mqformula} \usepackage{mqformula}
\usepackage{pkg/mqperiodictable} \usepackage{mqperiodictable}
\title{Formelsammlung} \title{Formelsammlung}
@ -127,7 +121,7 @@
\input{util/translations.tex} \input{util/translations.tex}
% \InputOnly{comp} % \InputOnly{cm}
\Input{math/math} \Input{math/math}
\Input{math/linalg} \Input{math/linalg}

4
src/math/calculus.tex
View File

@ -170,7 +170,7 @@
x^{\log(y)} &= y^{\log(x)} x^{\log(y)} &= y^{\log(x)}
} }
\end{formula} \end{formula}
\begin{formula}{intergral} \begin{formula}{integral}
\desc{Integral of natural logarithm}{}{} \desc{Integral of natural logarithm}{}{}
\desc[german]{Integral des natürluchen Logarithmus}{}{} \desc[german]{Integral des natürluchen Logarithmus}{}{}
\eq{ \eq{
@ -253,7 +253,7 @@
\ger{Liste nützlicher Integrale} \ger{Liste nützlicher Integrale}
]{list} ]{list}
% Put links to other integrals here % Put links to other integrals here
\fqEqRef{cal:log:integral} \fRef{math:cal:log:integral}
\begin{formula}{arcfunctions} \begin{formula}{arcfunctions}
\desc{Arcsine, arccosine, arctangent}{}{} \desc{Arcsine, arccosine, arctangent}{}{}

41
src/math/probability_theory.tex
View File

@ -13,8 +13,8 @@
\begin{formula}{variance} \begin{formula}{variance}
\absLabel \absLabel
\desc{Variance}{Square of the \fqEqRef{math:pt:std-deviation}}{} \desc{Variance}{Square of the \fRef{math:pt:std-deviation}}{}
\desc[german]{Varianz}{Quadrat der\fqEqRef{math:pt:std-deviation}}{} \desc[german]{Varianz}{Quadrat der\fRef{math:pt:std-deviation}}{}
\eq{\sigma^2 = (\Delta \hat{x})^2 = \Braket{\hat{x}^2} - \braket{\hat{x}}^2 = \braket{(x - \braket{x})^2}} \eq{\sigma^2 = (\Delta \hat{x})^2 = \Braket{\hat{x}^2} - \braket{\hat{x}}^2 = \braket{(x - \braket{x})^2}}
\end{formula} \end{formula}
@ -172,7 +172,7 @@
\begin{bigformula}{gamma} \begin{bigformula}{gamma}
\absLabel[gamma_distribution] \absLabel[gamma_distribution]
\desc{Gamma Distribution}{with $\lambda$ parameter}{$\Gamma$ \fqEqRef{math:cal:integral:list:gamma}, $\gamma$ \fqEqRef{math:cal:integral:list:lower_incomplete_gamma_function}} \desc{Gamma Distribution}{with $\lambda$ parameter}{$\Gamma$ \fRef{math:cal:integral:list:gamma_function}, $\gamma$ \fRef{math:cal:integral:list:lower_incomplete_gamma_function}}
\desc[german]{Gamma Verteilung}{mit $\lambda$ Parameter}{} \desc[german]{Gamma Verteilung}{mit $\lambda$ Parameter}{}
\begin{minipage}{\distleftwidth} \begin{minipage}{\distleftwidth}
\begin{figure}[H] \begin{figure}[H]
@ -191,7 +191,8 @@
\end{bigformula} \end{bigformula}
\begin{bigformula}{beta} \begin{bigformula}{beta}
\desc{Beta Distribution}{}{$\txB$ \fqEqRef{math:cal:integral:list:beta_function} / \fqEqRef{math:cal:integral:list:incomplete_beta_function}} \absLabel[beta_distribution]
\desc{Beta Distribution}{}{$\txB$ \fRef{math:cal:integral:list:beta_function} / \fRef{math:cal:integral:list:incomplete_beta_function}}
\desc[german]{Beta Verteilung}{}{} \desc[german]{Beta Verteilung}{}{}
\begin{minipage}{\distleftwidth} \begin{minipage}{\distleftwidth}
\begin{figure}[H] \begin{figure}[H]
@ -216,11 +217,12 @@
\ger{Diskrete Wahrscheinlichkeitsverteilungen} \ger{Diskrete Wahrscheinlichkeitsverteilungen}
]{discrete} ]{discrete}
\begin{bigformula}{binomial} \begin{bigformula}{binomial}
\absLabel[binomial_distribution]
\desc{Binomial distribution}{}{} \desc{Binomial distribution}{}{}
\desc[german]{Binomialverteilung}{}{} \desc[german]{Binomialverteilung}{}{}
\begin{ttext} \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}} \eng{For the number of trials going to infinity ($n\to\infty$), the binomial distribution converges to the \absRef[poisson distribution]{poisson_distribution}}
\ger{Geht die Zahl der Versuche gegen unendlich ($n\to\infty$), konvergiert die Binomualverteilung gegen die \hyperref[sec:pb:distributions:poisson]{Poissonverteilung}} \ger{Geht die Zahl der Versuche gegen unendlich ($n\to\infty$), konvergiert die Binomualverteilung gegen die \absRef[Poissonverteilung]{poisson_distribution}}
\end{ttext}\\ \end{ttext}\\
\begin{minipage}{\distleftwidth} \begin{minipage}{\distleftwidth}
\begin{figure}[H] \begin{figure}[H]
@ -240,6 +242,7 @@
\end{bigformula} \end{bigformula}
\begin{bigformula}{poisson} \begin{bigformula}{poisson}
\absLabel[poisson_distribution]
\desc{Poisson distribution}{}{} \desc{Poisson distribution}{}{}
\desc[german]{Poissonverteilung}{}{} \desc[german]{Poissonverteilung}{}{}
\begin{minipage}{\distleftwidth} \begin{minipage}{\distleftwidth}
@ -296,8 +299,8 @@
\ger{Fehlerfortpflanzung} \ger{Fehlerfortpflanzung}
]{error} ]{error}
\begin{formula}{generalised} \begin{formula}{generalised}
\desc{Generalized error propagation}{}{$V$ \fqEqRef{math:pt:covariance} matrix, $J$ \fqEqRef{math:cal:jacobi-matrix}} \desc{Generalized error propagation}{}{$V$ \fRef{math:pt:covariance} matrix, $J$ \fRef{math:cal:jacobi-matrix}}
\desc[german]{Generalisiertes Fehlerfortpflanzungsgesetz}{$V$ \fqEqRef{math:pt:covariance} Matrix, $J$ \fqEqRef{cal:jacobi-matrix}}{} \desc[german]{Generalisiertes Fehlerfortpflanzungsgesetz}{$V$ \fRef{math:pt:covariance} Matrix, $J$ \fRef{cal:jacobi-matrix}}{}
\eq{V_y = J(x) \cdot V_x \cdot J^{\T} (x)} \eq{V_y = J(x) \cdot V_x \cdot J^{\T} (x)}
\end{formula} \end{formula}
@ -308,19 +311,19 @@
\end{formula} \end{formula}
\begin{formula}{weight} \begin{formula}{weight}
\desc{Weight}{Variance is a possible choice for a weight}{$\sigma$ \fqEqRef{math:pt:variance}} \desc{Weight}{Variance is a possible choice for a weight}{$\sigma$ \fRef{math:pt:variance}}
\desc[german]{Gewicht}{Varianz ist eine mögliche Wahl für ein Gewicht}{} \desc[german]{Gewicht}{Varianz ist eine mögliche Wahl für ein Gewicht}{}
\eq{w_i = \frac{1}{\sigma_i^2}} \eq{w_i = \frac{1}{\sigma_i^2}}
\end{formula} \end{formula}
\begin{formula}{weighted-mean} \begin{formula}{weighted-mean}
\desc{Weighted mean}{}{$w_i$ \fqEqRef{math:pt:error:weight}} \desc{Weighted mean}{}{$w_i$ \fRef{math:pt:error:weight}}
\desc[german]{Gewichteter Mittelwert}{}{} \desc[german]{Gewichteter Mittelwert}{}{}
\eq{\overline{x} = \frac{\sum_{i} (x_i w_i)}{\sum_i w_i}} \eq{\overline{x} = \frac{\sum_{i} (x_i w_i)}{\sum_i w_i}}
\end{formula} \end{formula}
\begin{formula}{weighted-mean-error} \begin{formula}{weighted-mean-error}
\desc{Variance of weighted mean}{}{$w_i$ \fqEqRef{math:pt:error:weight}} \desc{Variance of weighted mean}{}{$w_i$ \fRef{math:pt:error:weight}}
\desc[german]{Varianz des gewichteten Mittelwertes}{}{} \desc[german]{Varianz des gewichteten Mittelwertes}{}{}
\eq{\sigma^2_{\overline{x}} = \frac{1}{\sum_i w_i}} \eq{\sigma^2_{\overline{x}} = \frac{1}{\sum_i w_i}}
\end{formula} \end{formula}
@ -330,18 +333,18 @@
\ger{Maximum likelihood Methode} \ger{Maximum likelihood Methode}
]{mle} ]{mle}
\begin{formula}{likelihood} \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{Likelihood function}{Likelihood of observing $x$ when parameter is $\theta$\\in general not normalized!}{$\rho$ \fRef{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} \desc[german]{Likelihood Funktion}{"Plausibilität" $x$ zu messen, wenn der Parameter $\theta$ ist\\nicht normalisiert!}{$\rho$ \fRef{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)} \eq{L:\Theta \rightarrow [0,1], \quad \theta \mapsto \rho(x|\theta)}
\end{formula} \end{formula}
\begin{formula}{likelihood_independant} \begin{formula}{likelihood_independant}
\desc{Likelihood function}{for independent and identically distributed random variables}{$x_i$ $n$ random variables, $\rho$ \fqEqRef{math:pt:pdf} $x\mapsto f(x|\theta)$ depending on parameter $\theta$} \desc{Likelihood function}{for independent and identically distributed random variables}{$x_i$ $n$ random variables, $\rho$ \fRef{math:pt:pdf} $x\mapsto f(x|\theta)$ depending on parameter $\theta$}
\desc[german]{Likelihood function}{für unabhängig und identisch verteilte Zufallsvariablen}{$x_i$ $n$ Zufallsvariablen$\rho$ \fqEqRef{math:pt:pdf} $x\mapsto f(x|\theta)$ hängt ab von Parameter $\theta$} \desc[german]{Likelihood function}{für unabhängig und identisch verteilte Zufallsvariablen}{$x_i$ $n$ Zufallsvariablen$\rho$ \fRef{math:pt:pdf} $x\mapsto f(x|\theta)$ hängt ab von Parameter $\theta$}
\eq{L(\theta) = \prod_{i=1}^n f(x_i;\theta)} \eq{L(\theta) = \prod_{i=1}^n f(x_i;\theta)}
\end{formula} \end{formula}
\begin{formula}{maximum_likelihood_estimate} \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{Maximum likelihood estimate (MLE)}{Paramater for which outcome is most likely}{$L$ \fRef{math:pt:mle:likelihood}, $\theta$ parameter of a \fRef{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}} \desc[german]{Maximum likelihood-Schätzung (MLE)}{Paramater, für den das Ergebnis am Wahrscheinlichsten ist}{$L$ \fRef{math:pt:mle:likelihood}, $\theta$ Parameter einer \fRef{math:pt:pdf}}
\eq{\theta_\text{ML} &= \argmax_\theta L(\theta)\\ &= \argmax_\theta \log \big(L(\theta)\big)} \eq{\theta_\text{ML} &= \argmax_\theta L(\theta)\\ &= \argmax_\theta \log \big(L(\theta)\big)}
\end{formula} \end{formula}
@ -356,13 +359,13 @@
\end{formula} \end{formula}
\begin{formula}{evidence} \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{Evidence}{}{$p(\mathcal{D}|\theta)$ \fRef{math:pt:mle:likelihood}, $p(\theta)$ \fRef{math:pt:bayesian:prior}, $\mathcal{D}$ data set}
% \desc[german]{}{}{} % \desc[german]{}{}{}
\eq{p(\mathcal{D}) = \int\d\theta \,p(\mathcal{D}|\theta)\,p(\theta)} \eq{p(\mathcal{D}) = \int\d\theta \,p(\mathcal{D}|\theta)\,p(\theta)}
\end{formula} \end{formula}
\begin{formula}{theorem} \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{Bayes' theorem}{}{$p(\theta|\mathcal{D})$ posterior distribution, $p(\mathcal{D}|\theta)$ \fRef{math:pt:mle:likelihood}, $p(\theta)$ \fRef{math:pt:bayesian:prior}, $p(\mathcal{D})$ \fRef{math:pt:bayesian:evidence}, $\mathcal{D}$ data set}
\desc[german]{Satz von Bayes}{}{} \desc[german]{Satz von Bayes}{}{}
\eq{p(\theta|\mathcal{D}) = \frac{p(\mathcal{D}|\theta)\,p(\theta)}{p(\mathcal{D})}} \eq{p(\theta|\mathcal{D}) = \frac{p(\mathcal{D}|\theta)\,p(\theta)}{p(\mathcal{D})}}
\end{formula} \end{formula}

62
src/pkg/mqformula.sty
View File

@ -54,18 +54,16 @@
% Class defining commands shared by all formula environments % Class defining commands shared by all formula environments
% 1: key % 1: key
\newenvironment{formulainternal}[1]{ \newenvironment{formulainternal}[1]{
% TODO refactor, using fqname@enter and leave \mqfqname@enter{#1}
% TODO There is no real need to differentiate between fqnames and sections,
% TODO thus change the meaning of f: from formula to fqname and change sec to f
% [1]: language % [1]: language
% 2: name % 2: name
% 3: description % 3: description
% 4: definitions/links % 4: definitions/links
\newcommand{\desc}[4][english]{ \newcommand{\desc}[4][english]{
% language, name, description, definitions % language, name, description, definitions
\ifblank{##2}{}{\dt[#1]{##1}{##2}} \ifblank{##2}{}{\dt{##1}{##2}}
\ifblank{##3}{}{\dt[#1_desc]{##1}{##3}} \ifblank{##3}{}{\dt[desc]{##1}{##3}}
\ifblank{##4}{}{\dt[#1_defs]{##1}{##4}} \ifblank{##4}{}{\dt[defs]{##1}{##4}}
} }
\directlua{n_formulaEntries = 0} \directlua{n_formulaEntries = 0}
@ -73,12 +71,12 @@
% [1]: label to use % [1]: label to use
% 2: Abbreviation to use for references % 2: Abbreviation to use for references
\newcommand{\abbrLabel}[2][#1]{ \newcommand{\abbrLabel}[2][#1]{
\abbrLink[f:\fqname:#1]{##1}{##2} \abbrLink[\fqname]{##1}{##2}
} }
% makes this formula referencable with \absRef{<name>} % makes this formula referencable with \absRef{<name>}
% [1]: label to use % [1]: label to use
\newcommand{\absLabel}[1][#1]{ \newcommand{\absLabel}[1][#1]{
\absLink[\fqname:#1]{f:\fqname:#1}{##1} \absLink[\fqname]{\fqname}{##1}
} }
\newcommand{\newFormulaEntry}{ \newcommand{\newFormulaEntry}{
@ -98,18 +96,6 @@
##1 ##1
\end{align} \end{align}
} }
% 1: equation for alignat environment
\newcommand{\eqAlignedAt}[2]{
\newFormulaEntry
\begin{flalign}%
\TODO{\text{remove macro}}
% dont place label when one is provided
% \IfSubStringInString{label}\unexpanded{#3}{}{
% \label{eq:#1}
% }
##1%
\end{flalign}
}
% 1: equation for flalign environment % 1: equation for flalign environment
\newcommand{\eqFLAlign}[2]{ \newcommand{\eqFLAlign}[2]{
\newFormulaEntry \newFormulaEntry
@ -127,7 +113,7 @@
\includegraphics{##1} \includegraphics{##1}
} }
% 1: content for the ttext environment % 1: content for the ttext environment
\newcommand{\ttxt}[2][#1:desc]{ \newcommand{\ttxt}[2][text]{
\newFormulaEntry \newFormulaEntry
\begin{ttext}[##1] \begin{ttext}[##1]
##2 ##2
@ -141,6 +127,9 @@
\newFormulaEntry \newFormulaEntry
\quantity@print{#1} \quantity@print{#1}
} }
\newcommand{\hiddenQuantity}[3]{%
\quantity@new[\fqname]{#1}{##1}{##2}{##3}
}
% must be used only in third argument of "constant" command % must be used only in third argument of "constant" command
% 1: value % 1: value
@ -159,20 +148,21 @@
\newFormulaEntry \newFormulaEntry
\constant@print{#1} \constant@print{#1}
} }
}{} }{
\mqfqname@leave
}
\newenvironment{formula}[1]{ \newenvironment{formula}[1]{
\begin{formulainternal}{#1} \begin{formulainternal}{#1}
\begingroup \begingroup
\label{f:\fqname:#1} \mqfqname@label
\storeLabel{\fqname:#1} % write label witout type prefix to aux file
\par\noindent\ignorespaces \par\noindent\ignorespaces
% \textcolor{gray}{\hrule} % \textcolor{gray}{\hrule}
% \vspace{0.5\baselineskip} % \vspace{0.5\baselineskip}
\NameWithDescription[\descwidth]{\fqname:#1}{\fqname:#1_desc} \NameWithDescription[\descwidth]{\fqname}{\fqname:desc}
\hfill \hfill
\begin{ContentBoxWithExplanation}{\fqname:#1_defs} \begin{ContentBoxWithExplanation}{\fqname:defs}
}{ }{
\end{ContentBoxWithExplanation} \end{ContentBoxWithExplanation}
\endgroup \endgroup
@ -188,33 +178,28 @@
\newenvironment{bigformula}[1]{ \newenvironment{bigformula}[1]{
\begin{formulainternal}{#1} \begin{formulainternal}{#1}
\edef\tmpFormulaName{#1}
\par\noindent \par\noindent
\begin{minipage}{\textwidth} % using a minipage to now allow line breaks within the bigformula \begin{minipage}{\textwidth} % using a minipage to now allow line breaks within the bigformula
\label{f:\fqname:#1} \mqfqname@label
\storeLabel{\fqname:#1} % write label witout type prefix to aux file
\par\noindent\ignorespaces \par\noindent\ignorespaces
% \textcolor{gray}{\hrule} % \textcolor{gray}{\hrule}
% \vspace{0.5\baselineskip} % \vspace{0.5\baselineskip}
\textbf{ \textbf{
\IfTranslationExists{\fqname:#1}{% \raggedright
\raggedright \GT{\fqname}
\GT{\fqname:#1}
}{\detokenize{#1}}
} }
\IfTranslationExists{\fqname:#1_desc}{ \IfTranslationExists{\fqname:desc}{
: {\color{fg1} \GT{\fqname:#1_desc}} : {\color{fg1} \GT{\fqname:desc}}
}{} }{}
\hfill \hfill
\par \par
}{ }{
\edef\tmpContentDefs{\fqname:\tmpFormulaName_defs} \IfTranslationExists{\fqname:defs}{%
\IfTranslationExists{\tmpContentDefs}{%
\smartnewline \smartnewline
\noindent \noindent
\begingroup \begingroup
\color{fg1} \color{fg1}
\GT{\tmpContentDefs} \GT{\fqname:defs}
% \edef\temp{\GT{#1_defs}} % \edef\temp{\GT{#1_defs}}
% \expandafter\StrSubstitute\expandafter{\temp}{:}{\\} % \expandafter\StrSubstitute\expandafter{\temp}{:}{\\}
\endgroup \endgroup
@ -230,7 +215,6 @@
\newenvironment{hiddenformula}[1]{ \newenvironment{hiddenformula}[1]{
\begin{formulainternal}{#1} \begin{formulainternal}{#1}
\renewcommand{\eq}[1]{} \renewcommand{\eq}[1]{}
\renewcommand{\eqAlignedAt}[2]{}
\renewcommand{\eqFLAlign}[2]{} \renewcommand{\eqFLAlign}[2]{}
\renewcommand{\fig}[2][1.0]{} \renewcommand{\fig}[2][1.0]{}
\renewcommand{\ttxt}[2][#1:desc]{} \renewcommand{\ttxt}[2][#1:desc]{}

193
src/pkg/mqfqname.sty
View File

@ -3,51 +3,70 @@
\RequirePackage{etoolbox} \RequirePackage{etoolbox}
\directlua{ \begin{luacode}
sections = sections or {} sections = sections or {}
function fqnameEnter(name) function fqnameEnter(name)
table.insert(sections, name) table.insert(sections, name)
% table.sort(sections) -- table.sort(sections)
end end
function fqnameLeave() function fqnameLeave()
if table.getn(sections) > 0 then if table.getn(sections) > 0 then
table.remove(sections) table.remove(sections)
end end
end end
function fqnameGet() function fqnameGet()
return table.concat(sections, ":") return table.concat(sections, ":")
end end
function fqnameLeaveOnlyFirstN(n) function fqnameLeaveOnlyFirstN(n)
if n >= 0 then if n >= 0 then
while table.getn(sections) > n do while table.getn(sections) > n do
table.remove(sections) table.remove(sections)
end
end end
end
end end
} \end{luacode}
\begin{luacode}
function fqnameGetDepth()
return table.getn(sections)
end
function fqnameGetN(N)
if N == nil or table.getn(sections) < N then
luatexbase.module_warning('fqnameGetN', 'N = ' .. N .. ' is larger then the table length')
return "?!?"
end
s = sections[1]
for i = 2, N do
s = s .. ":" .. sections[i]
end
return s
end
\end{luacode}
\newcommand{\mqfqname@update}{% \newcommand{\mqfqname@update}{%
\edef\fqname{\luavar{fqnameGet()}} \edef\fqname{\luavar{fqnameGet()}}
} }
\newcommand{\mqfqname@enter}[1]{% \newcommand{\mqfqname@enter}[1]{%
\directlua{fqnameEnter("\luaescapestring{#1}")}% \directlua{fqnameEnter("\luaescapestring{#1}")}%
\mqfqname@update \mqfqname@update
} }
\newcommand{\mqfqname@leave}{% \newcommand{\mqfqname@leave}{%
\directlua{fqnameLeave()}% \directlua{fqnameLeave()}%
\mqfqname@update \mqfqname@update
} }
\newcommand{\mqfqname@leaveOnlyFirstN}[1]{% \newcommand{\mqfqname@leaveOnlyFirstN}[1]{%
\directlua{fqnameLeaveOnlyFirstN(#1)}% \directlua{fqnameLeaveOnlyFirstN(#1)}%
} }
% SECTIONING % SECTIONING
% start <section>, get heading from translation, set label % start <section>, get heading from translation, set label
% secFqname is the fully qualified name of sections: the keys of all previous sections joined with a ':' % fqname is the fully qualified name of all sections and formulas, the keys of all previous sections joined with a ':'
% fqname is secFqname:<key> where <key> is the key/id of some environment, like formula % fqname is secFqname:<key> where <key> is the key/id of some environment, like formula
% [1]: code to run after setting \fqname, but before the \part, \section etc % [1]: code to run after setting \fqname, but before the \part, \section etc
% 2: key % 2: key
@ -55,164 +74,36 @@
\newpage \newpage
\mqfqname@leaveOnlyFirstN{0} \mqfqname@leaveOnlyFirstN{0}
\mqfqname@enter{#2} \mqfqname@enter{#2}
\edef\secFqname{\fqname}
#1 #1
% this is necessary so that \part/\section... takes the fully expanded string. Otherwise the pdf toc will have just the fqname % this is necessary so that \part/\section... takes the fully expanded string. Otherwise the pdf toc will have just the fqname
\edef\fqnameText{\GT{\fqname}} \edef\fqnameText{\GT{\fqname}}
\part{\fqnameText} \part{\fqnameText}
\label{sec:\fqname} \mqfqname@label
} }
\newcommand{\Section}[2][]{ \newcommand{\Section}[2][]{
\mqfqname@leaveOnlyFirstN{1} \mqfqname@leaveOnlyFirstN{1}
\mqfqname@enter{#2} \mqfqname@enter{#2}
\edef\secFqname{\fqname}
#1 #1
\edef\fqnameText{\GT{\fqname}} \edef\fqnameText{\GT{\fqname}}
\section{\fqnameText} \section{\fqnameText}
\label{sec:\fqname} \mqfqname@label
} }
\newcommand{\Subsection}[2][]{ \newcommand{\Subsection}[2][]{
\mqfqname@leaveOnlyFirstN{2} \mqfqname@leaveOnlyFirstN{2}
\mqfqname@enter{#2} \mqfqname@enter{#2}
\edef\secFqname{\fqname}
#1 #1
\edef\fqnameText{\GT{\fqname}} \edef\fqnameText{\GT{\fqname}}
\subsection{\fqnameText} \subsection{\fqnameText}
\label{sec:\fqname} \mqfqname@label
} }
\newcommand{\Subsubsection}[2][]{ \newcommand{\Subsubsection}[2][]{
\mqfqname@leaveOnlyFirstN{3} \mqfqname@leaveOnlyFirstN{3}
\mqfqname@enter{#2} \mqfqname@enter{#2}
\edef\secFqname{\fqname}
#1 #1
\edef\fqnameText{\GT{\fqname}} \edef\fqnameText{\GT{\fqname}}
\subsubsection{\fqnameText} \subsubsection{\fqnameText}
\label{sec:\fqname} \mqfqname@label
} }
\edef\fqname{NULL} \edef\fqname{NULL}
\newcommand\printFqName{\expandafter\detokenize\expandafter{\fqname}} \newcommand\printFqName{\expandafter\detokenize\expandafter{\fqname}}
\newcommand\luaDoubleFieldValue[3]{%
\directlua{
if #1 \string~= nil and #1[#2] \string~= nil and #1[#2][#3] \string~= nil then
tex.sprint(#1[#2][#3])
return
end
luatexbase.module_warning('luaDoubleFieldValue', 'Invalid indices to `#1`: `#2` and `#3`');
tex.sprint("???")
}%
}
% REFERENCES
% All xyzRef commands link to the key using the translated name
% Uppercase (XyzRef) commands have different link texts, but the same link target
% 1: key/fully qualified name (without qty/eq/sec/const/el... prefix)
% Equations/Formulas
% \newrobustcmd{\fqEqRef}[1]{%
\newrobustcmd{\fqEqRef}[1]{%
% \edef\fqeqrefname{\GT{#1}}
% \hyperref[eq:#1]{\fqeqrefname}
\hyperref[f:#1]{\GT{#1}}%
}
% Formula in the current section
\newrobustcmd{\secEqRef}[1]{%
% \edef\fqeqrefname{\GT{#1}}
% \hyperref[eq:#1]{\fqeqrefname}
\hyperref[f:\secFqname:#1]{\GT{\secFqname:#1}}%
}
% Section
% <name>
\newrobustcmd{\fqSecRef}[1]{%
\hyperref[sec:#1]{\GT{#1}}%
}
% Quantities
% <symbol>
\newrobustcmd{\qtyRef}[1]{%
\edef\tempname{\luaDoubleFieldValue{quantities}{"#1"}{"linkto"}}%
\hyperref[qty:#1]{\GT{\tempname:#1}}%
}
% <symbol> <name>
\newrobustcmd{\QtyRef}[1]{%
$\luaDoubleFieldValue{quantities}{"#1"}{"symbol"}$ \qtyRef{#1}%
}
% Constants
% <name>
\newrobustcmd{\constRef}[1]{%
\edef\tempname{\luaDoubleFieldValue{constants}{"#1"}{"linkto"}}%
\hyperref[const:#1]{\GT{\tempname:#1}}%
}
% <symbol> <name>
\newrobustcmd{\ConstRef}[1]{%
$\luaDoubleFieldValue{constants}{"#1"}{"symbol"}$ \constRef{#1}%
}
% Element from periodic table
% <symbol>
\newrobustcmd{\elRef}[1]{%
\hyperref[el:#1]{{\color{fg0}#1}}%
}
% <name>
\newrobustcmd{\ElRef}[1]{%
\hyperref[el:#1]{\GT{el:#1}}%
}
% "LABELS"
% These currently do not place a label,
% instead they provide an alternative way to reference an existing label
\directLuaAux{
absLabels = absLabels or {}
abbrLabels = abbrLabel or {}
}
% [1]: translation key, if different from target
% 2: target (fqname to point to)
% 3: key
\newcommand{\absLink}[3][\relax]{
\directLuaAuxExpand{
absLabels["#3"] = {}
absLabels["#3"]["fqname"] = [[#2]]
absLabels["#3"]["translation"] = [[#1]] or [[#2]]
% if [[#1]] == "" then
% absLabels["#3"]["translation"] = [[#2]]
% else
% absLabels["#3"]["translation"] = [[#1]]
% end
}
}
% [1]: target (fqname to point to)
% 2: key
% 3: label (abbreviation)
\newcommand{\abbrLink}[3][sec:\fqname]{
\directLuaAuxExpand{
abbrLabels["#2"] = {}
abbrLabels["#2"]["abbr"] = [[#3]]
abbrLabels["#2"]["fqname"] = [[#1]]
}
}
% [1]: text
% 2: key
\newcommand{\absRef}[2][]{%
\directlua{
if absLabels["#2"] == nil then
tex.sprint(string.sanitize(\luastring{#2}) .. "???")
else
if \luastring{#1} == "" then %-- if [#1] is not given, use translation of key as text, else us given text
tex.sprint("\\hyperref[" .. absLabels["#2"]["fqname"] .. "]{\\GT{" .. absLabels["#2"]["translation"] .. "}}")
else
tex.sprint("\\hyperref[" .. absLabels["#2"]["fqname"] .. "]{\luaescapestring{#1}}")
end
end
}
}
\newrobustcmd{\abbrRef}[1]{%
\directlua{
if abbrLabels["#1"] == nil then
tex.sprint(string.sanitize(\luastring{#1}) .. "???")
else
tex.sprint("\\hyperref[" .. abbrLabels["#1"]["fqname"] .. "]{" .. abbrLabels["#1"]["abbr"] .. "}")
end
}
}

22
src/pkg/mqlua.sty
View File

@ -6,13 +6,17 @@
\newcommand\luavar[1]{\directlua{tex.sprint(#1)}} \newcommand\luavar[1]{\directlua{tex.sprint(#1)}}
\begin{luacode*} \begin{luacode*}
function warning(message) function warning(fname, message)
-- Get the current file name and line number -- Get the current file name and line number
-- local info = debug.getinfo(2, "Sl") -- local info = debug.getinfo(2, "Sl")
-- local file_name = info.source -- local file_name = info.source
-- local line_number = info.currentline -- local line_number = info.currentline
-- tex.error(string.format("Warning %s at %s:%d", message, file_name, line_number)) -- tex.error(string.format("Warning %s at %s:%d", message, file_name, line_number))
texio.write("\nWARNING: " .. message .. "\n") if message == nil then
texio.write("\nWARNING: " .. fname .. "\n")
else
texio.write("\nWARNING: in " .. fname .. ":" .. message .. "\n")
end
end end
OUTDIR = os.getenv("TEXMF_OUTPUT_DIRECTORY") or "." OUTDIR = os.getenv("TEXMF_OUTPUT_DIRECTORY") or "."
@ -22,17 +26,15 @@ function fileExists(file)
if f then f:close() end if f then f:close() end
return f ~= nil return f ~= nil
end end
warning("TEST") warning("TEST")
\end{luacode*} \end{luacode*}
% units: siunitx units arguments, possibly chained by '=' % units: siunitx units arguments, possibly chained by '='
% returns: 1\si{unit1} = 1\si{unit2} = ... % returns: 1\si{unit1} = 1\si{unit2} = ...
\directlua{ \begin{luacode*}
function split_and_print_units(units) function split_and_print_units(units)
if units == nil then if units == nil then
tex.print("1") tex.sprint("1")
return return
end end
@ -47,20 +49,20 @@ function split_and_print_units(units)
end end
tex.print(result) tex.print(result)
end end
} \end{luacode*}
% STRING UTILITY % STRING UTILITY
\luadirect{ \begin{luacode*}
function string.startswith(s, start) function string.startswith(s, start)
return string.sub(s,1,string.len(start)) == start return string.sub(s,1,string.len(start)) == start
end end
function string.sanitize(s) function string.sanitize(s)
% -- Use gsub to replace the specified characters with an empty string -- Use gsub to replace the specified characters with an empty string
local result = s:gsub("[_^&]", " ") local result = s:gsub("[_^&]", " ")
return result return result
end end
} \end{luacode*}
% Write directlua command to aux and run it as well % Write directlua command to aux and run it as well
% This one expands the argument in the aux file: % This one expands the argument in the aux file:
\newcommand\directLuaAuxExpand[1]{ \newcommand\directLuaAuxExpand[1]{

258
src/pkg/mqref.sty Normal file
View File

@ -0,0 +1,258 @@
\ProvidesPackage{mqref}
\RequirePackage{mqlua}
\RequirePackage{mqfqname}
\newcommand\luaDoubleFieldValue[3]{%
\directlua{
if #1 \string~= nil and #1[#2] \string~= nil and #1[#2][#3] \string~= nil then
tex.sprint(#1[#2][#3])
return
end
luatexbase.module_warning('luaDoubleFieldValue', 'Invalid indices to `#1`: `#2` and `#3`');
tex.sprint("???")
}%
}
% LABELS
\begin{luacode}
-- Contains <label>: <true> for defined labels
-- This could later be extended to contain a list of all fqnames that
-- reference the label to make a network of references or sth like that
labels = labels or {}
-- Table of all labels that dont exist but were referenced
-- <label>: <fqname where it was referenced>
missingLabels = {}
-- aux file with labels for completion in vim
labelsFilepath = OUTDIR .. "/labels.txt" or "/tmp/labels.txt"
labelsLuaFilepath = OUTDIR .. "/labels.lua.txt" or "/tmp/labels.lua.txt"
-- aux file for debugging
missingLabelsFilepath = OUTDIR .. "/missing-labels.txt" or "/tmp/missing-labels.txt"
function labelExists(label)
if labels[label] == nil then return false else return true end
end
function labelSet(label)
labels[label] = true
end
if fileExists(labelsLuaFilepath) then
labels = dofile(labelsLuaFilepath) or {}
end
\end{luacode}
\begin{luacode*}
function serializeKeyValues(tbl)
local result = {}
-- sort by keys making a new table with keys as values and sorting that
for k, v in pairs(tbl) do
table.insert(result, k)
end
table.sort(result)
s = ""
for i, k in ipairs(result) do
s = s .. k .. "\tin\t" .. tbl[k] .. "\n"
end
return s
end
function dumpTableKeyValues(tableobj, filepath)
table.sort(tableobj)
local file = io.open(filepath, "w")
file:write(serializeKeyValues(tableobj))
file:close()
end
function serializeKeys(tbl)
local result = {}
-- sort by keys making a new table with keys as values and sorting that
for k, v in pairs(tbl) do
table.insert(result, k)
end
table.sort(result)
return table.concat(result, "\n")
end
function dumpTableKeys(tableobj, filepath)
table.sort(tableobj)
local file = io.open(filepath, "w")
file:write(serializeKeys(tableobj))
file:close()
end
\end{luacode*}
\AtEndDocument{\directlua{dumpTableKeys(labels, labelsFilepath)}}
\AtEndDocument{\directlua{dumpTable(labels, labelsLuaFilepath)}}
\AtEndDocument{\directlua{dumpTableKeyValues(missingLabels, missingLabelsFilepath)}}
% Set a label and write the label to the aux file
% [1]
\newcommand\mqfqname@label[1][\fqname]{
\label{#1}
\directlua{labelSet(\luastring{#1})}
}
% REFERENCES
% All xyzRef commands link to the key using the translated name
% Uppercase (XyzRef) commands have different link texts, but the same link target
% 1: key/fully qualified name (without qty/eq/sec/const/el... prefix)
\begin{luacode*}
function hyperref(target, text)
local s = ""
if labelExists(target) then
s = "\\hyperref[" .. target .. "]"
else -- mark as missing and referenced in current section
missingLabels[target] = fqnameGet()
end
if text == "" then
tex.sprint(s .. "{" .. tlGetFallbackCurrent(target) .. "}")
else
tex.sprint(s .. "{" .. text .. "}")
end
end
\end{luacode*}
% Equations/Formulas
% \newrobustcmd{\fqEqRef}[1]{%
\newrobustcmd{\fAbsRef}[2][]{%
\directlua{hyperref(\luastring{#2}, \luastring{#1})}%
}
\begin{luacode*}
function translateRelativeFqname(target)
local relN = 0
local relTarget = ""
warning('translateRelativeFqname', '(target=' .. target .. ') ');
for i = 1, #target do
local c = target:sub(i,i)
if c == ":" then
relN = relN + 1
else
relTarget = target:sub(i,#target)
break
end
end
if relN == 0 then
return target
end
local N = fqnameGetDepth()
local newtarget = fqnameGetN(N - relN + 1) .. ":" .. relTarget
warning('translateRelativeFqname', '(relN=' .. relN .. ') ' .. newtarget);
return newtarget
end
\end{luacode*}
\newcommand{\fRef}[2][]{
\directlua{hyperref(translateRelativeFqname(\luastring{#2}), \luastring{#1})}
}
% [1]: link text
% 2: number of steps to take up
% 3: link target relative to the previous fqname section
\newcommand{\mqfqname@fRelRef}[3][1]{
\directlua{
local N = fqnameGetDepth()
luatexbase.module_warning('fRelRef', '(N=' .. N .. ') #2');
if N > #2 then
local upfqname = fqnameGetN(N-#2)
hyperref(upfqname .. \luastring{:#3}, \luastring{#1})
else
luatexbase.module_warning('fUpRef', 'fqname depth (N=' .. N .. ') too low for fUpRef if #1');
end
}
}
\newcommand{\fThisRef}[2][]{\mqfqname@fRelRef[#1]{0}{#2}}
\newcommand{\fUpRef}[2][]{\mqfqname@fRelRef[#1]{1}{#2}}
\newcommand{\fUppRef}[2][]{\mqfqname@fRelRef[#1]{2}{#2}}
% Quantities
% <symbol>
\newrobustcmd{\qtyRef}[1]{%
\edef\tempname{\luaDoubleFieldValue{quantities}{"#1"}{"linkto"}}%
\hyperref[qty:#1]{\GT{\tempname:#1}}%
}
% <symbol> <name>
\newrobustcmd{\QtyRef}[1]{%
$\luaDoubleFieldValue{quantities}{"#1"}{"symbol"}$ \qtyRef{#1}%
}
% Constants
% <name>
\newrobustcmd{\constRef}[1]{%
\edef\tempname{\luaDoubleFieldValue{constants}{"#1"}{"linkto"}}%
\hyperref[const:#1]{\GT{\tempname:#1}}%
}
% <symbol> <name>
\newrobustcmd{\ConstRef}[1]{%
$\luaDoubleFieldValue{constants}{"#1"}{"symbol"}$ \constRef{#1}%
}
% Element from periodic table
% <symbol>
\newrobustcmd{\elRef}[1]{%
\hyperref[el:#1]{{\color{fg0}#1}}%
}
% <name>
\newrobustcmd{\ElRef}[1]{%
\hyperref[el:#1]{\GT{el:#1}}%
}
% "LABELS"
% These currently do not place a label,
% instead they provide an alternative way to reference an existing label
\directLuaAux{
absLabels = absLabels or {}
abbrLabels = abbrLabel or {}
}
% [1]: translation key, if different from target
% 2: target (fqname to point to)
% 3: key
\newcommand{\absLink}[3][\relax]{
\directLuaAuxExpand{
absLabels["#3"] = {}
absLabels["#3"]["fqname"] = [[#2]]
absLabels["#3"]["translation"] = [[#1]] or [[#2]]
% if [[#1]] == "" then
% absLabels["#3"]["translation"] = [[#2]]
% else
% absLabels["#3"]["translation"] = [[#1]]
% end
}
}
% [1]: target (fqname to point to)
% 2: key
% 3: label (abbreviation)
\newcommand{\abbrLink}[3][sec:\fqname]{
\directLuaAuxExpand{
abbrLabels["#2"] = {}
abbrLabels["#2"]["abbr"] = [[#3]]
abbrLabels["#2"]["fqname"] = [[#1]]
}
}
\newcommand{\fLabel}
% [1]: text
% 2: key
\newcommand{\absRef}[2][]{%
\directlua{
if absLabels["#2"] == nil then
tex.sprint(string.sanitize(\luastring{#2}) .. "???")
else
if \luastring{#1} == "" then %-- if [#1] is not given, use translation of key as text, else us given text
tex.sprint("\\hyperref[" .. absLabels["#2"]["fqname"] .. "]{\\GT{" .. absLabels["#2"]["translation"] .. "}}")
else
tex.sprint("\\hyperref[" .. absLabels["#2"]["fqname"] .. "]{\luaescapestring{#1}}")
end
end
}
}
\newrobustcmd{\abbrRef}[1]{%
\directlua{
if abbrLabels["#1"] == nil then
tex.sprint(string.sanitize(\luastring{#1}) .. "???")
else
tex.sprint("\\hyperref[" .. abbrLabels["#1"]["fqname"] .. "]{" .. abbrLabels["#1"]["abbr"] .. "}")
end
}
}

8
src/pkg/mqtranslation.sty
View File

@ -85,9 +85,9 @@
end end
function dumpTranslations() function dumpTable(tableobj, filepath)
local file = io.open(translationsFilepath, "w") local file = io.open(filepath, "w")
file:write("return " .. serialize(translations) .. "\n") file:write("return " .. serialize(tableobj) .. "\n")
file:close() file:close()
end end
@ -97,7 +97,7 @@
\end{luacode*} \end{luacode*}
\AtEndDocument{\directlua{dumpTranslations()}} \AtEndDocument{\directlua{dumpTable(translations, translationsFilepath)}}
% %
% TRANSLATION COMMANDS % TRANSLATION COMMANDS

2
src/qm/atom.tex
View File

@ -28,7 +28,7 @@
\end{formula} \end{formula}
\begin{formula}{wave_function} \begin{formula}{wave_function}
\desc{Wave function}{}{$R_{nl}(r)$ \fqEqRef{qm:h:radial}, $Y_{lm}$ \fqEqRef{qm:spherical_harmonics}} \desc{Wave function}{}{$R_{nl}(r)$ \fRef{qm:h:radial}, $Y_{lm}$ \fRef{qm:spherical_harmonics}}
\desc[german]{Wellenfunktion}{}{} \desc[german]{Wellenfunktion}{}{}
\eq{\psi_{nlm}(r, \theta, \phi) = R_{nl}(r)Y_{lm}(\theta,\phi)} \eq{\psi_{nlm}(r, \theta, \phi) = R_{nl}(r)Y_{lm}(\theta,\phi)}
\end{formula} \end{formula}

4
src/qm/qm.tex
View File

@ -562,7 +562,7 @@
\eq{H &= \underbrace{\hbar\omega_c \hat{a}^\dagger \hat{a}}_\text{\GT{field}} \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{\hbar\omega_\text{a} \frac{\hat{\sigma}_z}{2}}_\text{\GT{atom}}
+ \underbrace{\frac{\hbar\Omega}{2} \hat{E} \hat{S}}_\text{int} \\ + \underbrace{\frac{\hbar\Omega}{2} \hat{E} \hat{S}}_\text{int} \\
\shortintertext{\GT{after} \hyperref[eq:qm:other:RWA]{RWA}:} \\ \shortintertext{\GT{after} \fRef[RWA]{qm:other:RWA}:} \\
&= \hbar\omega_c \hat{a}^\dagger \hat{a} &= \hbar\omega_c \hat{a}^\dagger \hat{a}
+ \hbar\omega_\text{a} \hat{\sigma}^\dagger \hat{\sigma} + \hbar\omega_\text{a} \hat{\sigma}^\dagger \hat{\sigma}
+ \frac{\hbar\Omega}{2} (\hat{a}\hat{\sigma^\dagger} + \hat{a}^\dagger \hat{\sigma}) + \frac{\hbar\Omega}{2} (\hat{a}\hat{\sigma^\dagger} + \hat{a}^\dagger \hat{\sigma})
@ -572,7 +572,7 @@
\Section[ \Section[
\eng{Other} \eng{Other}
\ger{Sonstiges} \ger{Sonstiges}
]{other} ]{other}
\begin{formula}{RWA} \begin{formula}{RWA}
\desc{Rotating Wave Approximation (RWS)}{Rapidly oscilating terms are neglected}{$\omega_\text{L}$ light frequency, $\omega_0$ transition frequency} \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} \desc[german]{Rotating Wave Approximation / Drehwellennäherung (RWS)}{Schnell oscillierende Terme werden vernachlässigt}{$\omega_\text{L}$ Frequenz des Lichtes, $\omega_0$ Übergangsfrequenz}

7
src/quantities.tex
View File

@ -150,6 +150,13 @@
\quantity{\sigma}{\per\ohm\m}{} \quantity{\sigma}{\per\ohm\m}{}
\end{formula} \end{formula}
\begin{formula}{wave_vector}
\desc{Wavevector}{Vector perpendicular to the wavefront}{}
\desc[german]{Wellenvektor}{Vektor senkrecht zur Wellenfront}{}
\eq{\abs{k} = \frac{2\pi}{\lambda}}
\quantity{\vec{k}}{1\per\m}{v}
\end{formula}
\Subsection[ \Subsection[
\eng{Others} \eng{Others}
\ger{Sonstige} \ger{Sonstige}

4
src/quantum_computing.tex
View File

@ -276,8 +276,8 @@
\ger{Tunable Transmon Qubit} \ger{Tunable Transmon Qubit}
]{tunable} ]{tunable}
\begin{formula}{circuit} \begin{formula}{circuit}
\desc{Frequency tunable transmon}{By using a \fqSecRef{qc:scq:elements:squid} instead of a \fqSecRef{qc:scq:elements:josephson_junction}, the qubit is frequency tunable through an external field}{} \desc{Frequency tunable transmon}{By using a \fRef{qc:scq:elements:squid} instead of a \fRef{qc:scq:elements:josephson_junction}, the qubit is frequency tunable through an external field}{}
\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}{} \desc[german]{}{Durch Nutzung eines \fRef{qc:scq:elements:squid} anstatt eines \fRef{qc:scq:elements:josephson_junction}s, ist die Frequenz des Qubits durch ein externes Magnetfeld einstellbar}{}
\centering \centering
\begin{tikzpicture} \begin{tikzpicture}
% \draw (0,0) to[sV=$V_\text{g}$] ++(0,3) % \draw (0,0) to[sV=$V_\text{g}$] ++(0,3)

21
src/statistical_mechanics.tex
View File

@ -432,26 +432,31 @@
\desc{Internal energy}{}{} \desc{Internal energy}{}{}
\desc[german]{Innere Energie}{}{} \desc[german]{Innere Energie}{}{}
\eq{\d U(S,V,N) = T\d S -p\d V + \mu\d N} \eq{\d U(S,V,N) = T\d S -p\d V + \mu\d N}
\hiddenQuantity{U}{\joule}{s}
\end{formula} \end{formula}
\begin{formula}{free_energy} \begin{formula}{free_energy}
\desc{Free energy / Helmholtz energy }{}{} \desc{Free energy / Helmholtz energy }{}{}
\desc[german]{Freie Energie / Helmholtz Energie}{}{} \desc[german]{Freie Energie / Helmholtz Energie}{}{}
\eq{\d F(T,V,N) = -S\d T -p\d V + \mu\d N} \eq{\d F(T,V,N) = -S\d T -p\d V + \mu\d N}
\hiddenQuantity{F}{\joule}{s}
\end{formula} \end{formula}
\begin{formula}{enthalpy} \begin{formula}{enthalpy}
\desc{Enthalpy}{}{} \desc{Enthalpy}{}{}
\desc[german]{Enthalpie}{}{} \desc[german]{Enthalpie}{}{}
\eq{\d H(S,p,N) = T\d S +V\d p + \mu\d N} \eq{\d H(S,p,N) = T\d S +V\d p + \mu\d N}
\hiddenQuantity{H}{\joule}{s}
\end{formula} \end{formula}
\begin{formula}{gibbs_energy} \begin{formula}{gibbs_energy}
\desc{Free enthalpy / Gibbs energy}{}{} \desc{Free enthalpy / Gibbs energy}{}{}
\desc[german]{Freie Entahlpie / Gibbs-Energie}{}{} \desc[german]{Freie Entahlpie / Gibbs-Energie}{}{}
\eq{\d G(T,p,N) = -S\d T + V\d p + \mu\d N} \eq{\d G(T,p,N) = -S\d T + V\d p + \mu\d N}
\hiddenQuantity{G}{\joule}{s}
\end{formula} \end{formula}
\begin{formula}{grand_canon_pot} \begin{formula}{grand_canon_pot}
\desc{Grand canonical potential}{}{} \desc{Grand canonical potential}{}{}
\desc[german]{Großkanonisches Potential}{}{} \desc[german]{Großkanonisches Potential}{}{}
\eq{\d \Phi(T,V,\mu) = -S\d T -p\d V - N\d\mu} \eq{\d \Phi(T,V,\mu) = -S\d T -p\d V - N\d\mu}
\hiddenQuantity{\Phi}{\joule}{s}
\end{formula} \end{formula}
\TODO{Maxwell Relationen, TD Quadrat} \TODO{Maxwell Relationen, TD Quadrat}
@ -675,14 +680,14 @@
\eq{g_s = 2s+1} \eq{g_s = 2s+1}
\end{formula} \end{formula}
\begin{formula}{dos} \begin{formula}{dos}
\desc{Density of states}{}{$g_s$ \fqEqRef{td:id_qgas:spin_degeneracy_factor}} \desc{Density of states}{}{$g_s$ \fRef{td:id_qgas:spin_degeneracy_factor}}
\desc[german]{Zustandsdichte}{}{$g_s$ \fqEqRef{td:id_qgas:spin_degeneracy_factor}} \desc[german]{Zustandsdichte}{}{$g_s$ \fRef{td:id_qgas:spin_degeneracy_factor}}
\eq{g(\epsilon) = g_s \frac{V}{4\pi} \left(\frac{2m}{\hbar^2}\right)^\frac{3}{2} \sqrt{\epsilon}} \eq{g(\epsilon) = g_s \frac{V}{4\pi} \left(\frac{2m}{\hbar^2}\right)^\frac{3}{2} \sqrt{\epsilon}}
\end{formula} \end{formula}
\begin{formula}{occupation_number_per_e} \begin{formula}{occupation_number_per_e}
\desc{Occupation number per energy}{}{\fqEqRef{td:id_qgas:dos}, \bosfer} \desc{Occupation number per energy}{}{\fRef{td:id_qgas:dos}, \bosfer}
\desc[german]{Besetzungszahl pro Energie}{}{\fqEqRef{td:id_qgas:dos}, \bosfer} \desc[german]{Besetzungszahl pro Energie}{}{\fRef{td:id_qgas:dos}, \bosfer}
\eq{n(\epsilon)\, \d\epsilon &= \frac{g(\epsilon)}{\e^{\beta(\epsilon - \mu)} \mp 1}\,\d\epsilon} \eq{n(\epsilon)\, \d\epsilon &= \frac{g(\epsilon)}{\e^{\beta(\epsilon - \mu)} \mp 1}\,\d\epsilon}
\end{formula} \end{formula}
@ -797,8 +802,8 @@
\end{formula} \end{formula}
\begin{formula}{specific_density} \begin{formula}{specific_density}
\desc{Specific density}{}{$f$ \fqEqRef{td:id_qgas:generalized_zeta}, $g$ degeneracy factor, $z$ \fqEqRef{td:id_qgas:fugacity}} \desc{Specific density}{}{$f$ \fRef{td:id_qgas:generalized_zeta}, $g$ degeneracy factor, $z$ \fRef{td:id_qgas:fugacity}}
\desc[german]{Spezifische Dichte}{}{$f$ \fqEqRef{td:id_qgas:generalized_zeta}, $g$ Entartungsfaktor, $z$ \fqEqRef{td:id_qgas:fugacity}} \desc[german]{Spezifische Dichte}{}{$f$ \fRef{td:id_qgas:generalized_zeta}, $g$ Entartungsfaktor, $z$ \fRef{td:id_qgas:fugacity}}
\eq{v = \frac{N}{V} = \frac{g}{\lambda^3}f_{3/2}(z)} \eq{v = \frac{N}{V} = \frac{g}{\lambda^3}f_{3/2}(z)}
\end{formula} \end{formula}
@ -826,8 +831,8 @@
\end{formula} \end{formula}
\begin{formula}{heat_cap} \begin{formula}{heat_cap}
\desc{Heat capacity}{\gt{low_temps}}{differs from \fqEqRef{td:TODO:petit_dulong}} \desc{Heat capacity}{\gt{low_temps}}{differs from \fRef{td:TODO:petit_dulong}}
\desc[german]{Wärmecapacity}{\gt{low_temps}}{weicht ab vom \fqEqRef{td:TODO:petit_dulong}} \desc[german]{Wärmecapacity}{\gt{low_temps}}{weicht ab vom \fRef{td:TODO:petit_dulong}}
\fig{img/td_fermi_heat_capacity.pdf} \fig{img/td_fermi_heat_capacity.pdf}
\eq{C_V = \pdv{E}{T}_V = N\kB \frac{\pi}{2} \left(\frac{T}{T_\text{F}}\right)} \eq{C_V = \pdv{E}{T}_V = N\kB \frac{\pi}{2} \left(\frac{T}{T_\text{F}}\right)}
\end{formula} \end{formula}

2
src/test.tex
View File

@ -52,7 +52,7 @@ GT: {\textbackslash}ttest:name = \GT{\ttest:name}\\
\paragraph{Testing hyperrefs} \paragraph{Testing hyperrefs}
\noindent{This text is labeled with "test" \label{test}}\\ \noindent{This text is labeled with "test" \label{test}}\\
\hyperref[test]{This should refer to the line above}\\ \fRef[This should refer to the line above]{test}\\
Link to quantity which is defined after the reference: \qtyRef{test}\\ Link to quantity which is defined after the reference: \qtyRef{test}\\
\DT[eq:test]{english}{If you read this, then the translation for eq:test was expandend!} \DT[eq:test]{english}{If you read this, then the translation for eq:test was expandend!}
Link to defined quantity: \qtyRef{mass} Link to defined quantity: \qtyRef{mass}

12
src/util/environments.tex
View File

@ -43,12 +43,12 @@
% add links to some names % add links to some names
\directlua{ \directlua{
local cases = { local cases = {
pdf = "f:math:pt:pdf", pdf = "math:pt:pdf",
pmf = "f:math:pt:pmf", pmf = "math:pt:pmf",
cdf = "f:math:pt:cdf", cdf = "math:pt:cdf",
mean = "f:math:pt:mean", mean = "math:pt:mean",
variance = "f:math:pt:variance", variance = "math:pt:variance",
median = "f:math:pt:median", median = "math:pt:median",
} }
if cases["\luaescapestring{##1}"] \string~= nil then if cases["\luaescapestring{##1}"] \string~= nil then
tex.sprint("\\hyperref["..cases["\luaescapestring{##1}"].."]{\\GT{##1}}") tex.sprint("\\hyperref["..cases["\luaescapestring{##1}"].."]{\\GT{##1}}")