qcl-model: Created project, added mathematical model.

src/qcl-model/README.md

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+# qcl-model
+
+This project contains figures related to mathematical modelling of quantum
+cascade lasers.

src/qcl-model/math_model.tex

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+%
+% qclsip: The Quantum Cascade Laser Stock Image Project.
+%
+% Copyright (c) 2019, Computational Photonics Group, Technical University of
+% Munich.
+%
+% Mathematical model of a QCL (Schrödinger-Poisson, Ensemble Monte Carlo,
+% Maxwell's equation, Lindblad equation).
+% Created by Michael Riesch <[email protected]> (2019)
+%
+% This program is free software; you can redistribute it and/or modify
+% it under the terms of the GNU General Public License as published by
+% the Free Software Foundation; either version 3 of the License, or
+% (at your option) any later version.
+%
+% This program is distributed in the hope that it will be useful,
+% but WITHOUT ANY WARRANTY; without even the implied warranty of
+% MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
+% GNU General Public License for more details.
+%
+% You should have received a copy of the GNU General Public License
+% along with this program; if not, write to the Free Software Foundation,
+% Inc., 51 Franklin Street, Fifth Floor, Boston, MA 02110-1301 USA
+\documentclass[tikz]{standalone}
+
+\usepackage[utf8]{inputenc}
+\usepackage[T1]{fontenc}
+\usepackage{tikz}
+\usetikzlibrary{calc}
+
+% set colors
+\usepackage{xcolor}
+\definecolor{sipblue}{RGB}{0,101,189} % Pantone 300
+\definecolor{sipdarkblue}{RGB}{0,82,147} % Pantone 301
+\definecolor{siplightblue}{RGB}{152,198,234} % Pantone 283
+\definecolor{sipmedblue}{RGB}{100,160,200} % Pantone 542
+\definecolor{sipivory}{RGB}{218,215,203} % Pantone 7527
+\definecolor{sipgreen}{RGB}{162,173,0} % Pantone 383
+\definecolor{siporange}{RGB}{227,114,34} % Pantone 158
+\definecolor{sipgray}{gray}{0.6} % Gray 60%
+
+% set font
+\usepackage{helvet}
+\renewcommand{\familydefault}{\sfdefault}
+
+\begin{document}
+\begin{tikzpicture}
+ \tikzstyle{myline}=[very thick, line cap=round,line join=round];
+ \tikzstyle{mytext}=[draw, text=black, align=left];
+ \tikzstyle{myconn}=[myline, ->, >=stealth];
+
+ % static part
+ \node[mytext, myline, draw=siporange, anchor=north west] (sp) at (0, 7) {
+ \textcolor{siporange}{Energy levels}\\Schrödinger-Poisson equation};
+
+ \node[mytext, myline, draw=siporange, anchor=east] (mc) at (8, 5) {
+ \textcolor{siporange}{Carrier transport}\\Ensemble Monte Carlo (EMC)/\\
+ Density Matrix EMC};
+
+ % dynamic part
+ \node[mytext, myline, draw=sipblue, anchor=west] (lb) at (0, 3) {
+ \textcolor{sipblue}{Electron dynamics}\\Lindblad equation\\
+ $\partial_t \hat{\rho} = -\mathrm{i}\hbar^{-1} \left[ \hat{H}_0 -
+ \hat \mu E_z, \hat{\rho} \right] + \hat{\rho}_{\mathrm{diss}}$};
+
+ \node[mytext, myline, draw=sipblue, anchor=south east] (mw) at (8, 0) {
+ \textcolor{sipblue}{Optical field}\\Maxwell's equations in 1D\\
+ $\partial_t H_y = \mu^{-1} \partial_x E_z$\\
+ $\partial_t E_z = \epsilon^{-1} \left( -\sigma E_z - \partial_t P_z +
+ \partial_x H_y \right)$};
+
+ % connections
+ \draw[myconn, draw=siporange] (sp.east) to[bend left] node[midway, right] {
+ $E_i, \Psi_i$} (mc.north);
+
+ \draw[myconn, draw=siporange] (mc.west) to[bend left] node[midway, left] {
+ $f_i$} (sp.south);
+
+ \draw[myconn, draw=siporange] ($(sp.south west) + (1.1, 0)$)
+ -- node[midway, left] {$\hat H_0, \hat \mu$}
+ ($(lb.north west) + (1.1, 0)$);
+
+ \draw[myconn, draw=siporange] ($(mc.west) - (0, 0.3)$)
+ -| node[midway, left] {$\hat{\rho}_{\mathrm{diss}}$}
+ ($(lb.north) - (0.5, 0)$);
+
+ \draw[myconn, draw=sipblue] (mw.west)
+ to[bend left] node[midway, below, outer sep=3pt] {$E_z$}
+ ($(lb.south west) + (1.1, 0)$) ;
+
+ \draw[myconn, draw=sipblue] (lb.east)
+ to[bend left] node[midway, above, outer sep=3pt] {$\partial_t P_z$
+ % $= N \mathrm{Tr}\left\{\hat \mu \partial_t \hat \rho\right\}$
+ }
+ ($(mw.north east) - (1.1, 0)$);
+\end{tikzpicture}
+\end{document}