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@ -77,31 +77,34 @@ benchmark for HOPS and the results of \cref{chap:flow}.
The implementation and systematic application of this benchmark is
performed in \cref{chap:numres}. Further, the spin boson model will be
explored as an example of a system that is not exactly solvable in
general. This also gives us the first opportunity to discuss and
explore the intricacies of the interplay between system, interaction
and bath energy expectation values, as well as the flow of energy
between system and bath.
explored as an example of a system for which no analytic solution is
known. This also gives us the first opportunity to discuss and explore
the intricacies of the interplay between system, interaction and bath
energy expectation values, as well as the flow of energy between
system and bath.
Finally, we will turn to some thermodynamical questions in
\cref{sec:therm_results} both from a conceptual angle in
\cref{sec:basic_thermo} and through the exploration of concrete
systems in \cref{sec:singlemod,sec:otto}. Beginning with a review of
some bounds on energy extraction from systems coupled to infinite
baths the concept of ergotropy will be discussed and illustrated
baths, the concept of ergotropy will be discussed and illustrated
through a concrete calculation. Importantly, this requires us to take
a perspective that is centered on the global unitary evolution which
we have access to with HOPS. Subsequently, we will turn to
we have access to using HOPS. Subsequently, we will turn to
periodically modulated systems and explore both the capabilities of
HOPS, and the role of the aforementioned bounds in actual models.
The aim of this work is to demonstrate the validity of the HOPS
framework and its suitability for thermodynamical applications. In
this spirit quantum Brownian motion and spin-boson like models are
being explored to provide an overview of the capabilities of the
method and ideas for future studies. Although those are mentioned
throughout the work, some promising avenues are being highlighted in
\cref{cha:concl-ideas-future}.
In summary, the aim of this work is to demonstrate the validity of the
HOPS framework and its suitability for thermodynamical
applications. In this spirit quantum Brownian motion and spin-boson
like models are being explored to provide an overview of the
capabilities of the method and ideas for future studies. Although
those are mentioned throughout the work, some promising avenues are
being highlighted in \cref{cha:concl-ideas-future}.
We begin now, by setting the stage for main part of this work and
introducing some elementary notions in~\cref{sec:open_systems}.
\section{Open Quantum Systems}
\label{sec:open_systems}