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make intro for num_results nicer

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Valentin Boettcher 2022-09-21 17:29:55 +02:00
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@ -15,9 +15,20 @@ visible in all simulations will be discussed and explained in
\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}. There we will also look into the characteristics
of the flow depending on the shape of the spectral density.
able to obtain consistent results as is demonstrated upon the example
of the spin-boson model \cref{sec:prec_sim}. We will also look
into the characteristics of the energy flow between system and bath
depending on the shape of the spectral density. As the interaction
energy is not insubstantial in the regime that will be studied, we
turn off the interaction smoothly at the end of the evolution to be
able to adequately discuss our observations.
Finally, in \cref{sec:initial-slip-sb} we will study the short time
behavior of the spin-boson model, which will prove to be similar to
that of the harmonic oscillator discussed earlier. We will relate this
feature of the dynamics to the discussion in \cref{sec:pure_deph} and
also to the systematics of HOPS. Further, the effects of slowly and
smoothly turning on the interaction will be studied.
% These results will strengthen the confidence in
% the method so that we can turn to more complicated applications.
@ -25,6 +36,7 @@ of the flow depending on the shape of the spectral density.
% 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}.
\section{Some Remarks on the Methods}
\label{sec:meth}
Before we begin with the applications in earnest, let us review some
@ -1288,7 +1300,8 @@ the Redfield master equation does not require the secular
approximation, but only weak coupling and can therefore capture
non-Markovian dynamics.
\paragraph{Initial Slip}
\subsection{Initial Slip}
\label{sec:initial-slip-sb}
\begin{figure}[htp]
\centering
\includegraphics{figs/one_bath_syst/omega_initial_slip}