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roadmap for Applications chapter

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src/hops_tweak.tex
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@ -504,3 +504,7 @@ and
∫_0^t\dd{s}A(s)\qty(α(s)-α_0(s)) =\\
∑_{m,n}\frac{A_nG_m}{C_n+W_m}\qty(1-\eu^{-(C_n+W_m)t}) - ∑_{m,n}\frac{A_nU_m}{C_n+Q_m}\qty(1-\eu^{-(C_n+Q_m)t}).
\end{multline}
\subsection{Technical Notes on the Code}
\label{sec:code}

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src/num_results.tex
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@ -1,24 +1,28 @@
\chapter{Numerical Results}
\chapter{Applications}
\label{chap:numres}
\begin{itemize}
\item all the theory developed in \cref{chap:flow,chap:analytsol}
wants some applications
\item roadmap: first verify numerics and systematics using
\cref{chap:analytsol} in \cref{sec:hopsvsanalyt} and then using
energy conservation \cref{sec:prec_sim}. Although not the focus:
also some discussion of observations and the role of stronger
coupling and non-markovianity
\item especially short time behaviour in \cref{sec:pure_deph}
\item after systematics interlude about basic quantum-thermo
\cref{sec:basic_thermo}
\item finally short applications: single bath \cref{sec:singlemod} and
a simple otto cycle \cref{sec:otto}
\end{itemize}
In this chapter some application of the results described in
\cref{chap:flow,chap:analytsol} are presented. In
\cref{sec:hopsvsanalyt}, we begin by considering the bath energy for
an analytically solvable model and contrasting the analytical results
with the results obtained by hops.
After developing the tools for obtaining information about bath
related observables in \cref{chap:flow} and the means for their
verification in \cref{chap:analytsol}, we are now in a position to
apply those results.
The roadmap is the following. Using \cref{chap:analytsol} we will
verify the results of \cref{chap:flow} in \cref{sec:hopsvsanalyt}. A
striking phenomenon will be noticed and explained in a brief detour
\cref{sec:pure_deph}.
In the generic case where no analytic solution we nevertheless are
able to obtain consistent results as is demonstrated in
\cref{sec:prec_sim}.
These results will strengthen the confidence in
the method so that we can turn to more complicated applications.
First a brief overview of interesting features of quantum
thermodynamics is given in \cref{sec:basic_thermo}. Subsequently we
will turn to two applications to demonstrate these features in
\cref{sec:singlemod,sec:otto}.
An overview and explanation of the codes used in this chapter can be found
in \cref{sec:code}.
\section{Some Remarks on the Methods}
\label{sec:meth}