fix "in refs...."

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Valentin Boettcher 2022-09-27 15:08:01 +02:00
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7 changed files with 40 additions and 14 deletions

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@ -82,4 +82,30 @@ linkcolor=blue,
% cursive bold in maths
\unimathsetup{math-style=TeX,bold-style=ISO}
%% citing "in ref"
\NewBibliographyString{refname}
\NewBibliographyString{refsname}
\DefineBibliographyStrings{english}{%
refname = {Ref\adddot},
refsname = {Refs\adddot}
}
\DeclareCiteCommand{\refcite}
{%
\ifnum\thecitetotal=1
\bibstring{refname}%
\else%
\bibstring{refsname}%
\fi%
\addspace\bibopenbracket%
\usebibmacro{cite:init}%
\usebibmacro{prenote}}
{\usebibmacro{citeindex}%
\usebibmacro{cite:comp}}
{}
{\usebibmacro{cite:dump}%
\usebibmacro{postnote}%
\bibclosebracket}
\recalctypearea

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@ -235,7 +235,7 @@ temperature, as we are working in the Heisenberg picture.
For completeness, it may be of interest to find a solution for
negative times. This solution is relatively unphysical, as the initial
condition of a product state\footnote{For a treatment of more general
initial states see \cite{Grabert1988Oct}.} plays a pivotal role in
initial states see \refcite{Grabert1988Oct}.} plays a pivotal role in
open system dynamics~\cite{Rivas2012}. Therefore a system that starts
out in some entangled state just to reach the perfect product state at
\(t=0\) is not something that is likely to be applicable to physical

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@ -518,7 +518,7 @@ through energy conservation as in~\cite{Kato2016Dec}, we find
H_\inter^{(n)}]}
\end{equation}
regardless of the (non-) commutativity\footnote{For example, the
three-level model used in \cite{Uzdin2015Sep,Klatzow2019Mar} has
three-level model used in \refcite{Uzdin2015Sep,Klatzow2019Mar} has
non-commuting couplings.} of the interaction
Hamiltonians. Therefore, we can apply the formalism of the previous
sections almost unchanged, by taking care that all quantities involved

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@ -413,7 +413,7 @@ This leads to the nonlinear NMQSD equation~\cite{Diosi1998Mar}
-\ev{L^\dag}_{t}}_0^t\dd{s}α(t-s)\fdv{\ket{ψ({\tilde{η}}^\ast_t, t)}}{\tilde{η}^\ast_s}.
\end{equation}
There is a subtlety concerning the functional derivative that won't be
discussed here but in \cite{Hartmann2021Aug,RichardDiss} or
discussed here but in \refcite{Hartmann2021Aug,RichardDiss} or
\cref{sec:nonlin_flow}. Crucially, the system state is now recovered
through
\begin{equation}

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@ -1443,7 +1443,7 @@ with specific bath degrees of freedom which are independent themselves
except for their interaction with the system.
This interpretation is corroborated by a time discrete version of the
NMQSD discussed in \cite{RichardDiss}. There, the
NMQSD discussed in \refcite{RichardDiss}. There, the
\emph{Time-Oscillator picture} is introduced, which shows that a
variant of the NMQSD can be formulated as the successive interaction
in time of the system with mode like degrees of freedom. At each time
@ -1474,9 +1474,9 @@ Note that the short time behaviour discussed here can usually not be
resolved by the usual Markovian master equations. This is due to the
fact, that the bath timescale \(\sim 1/ω_{c}\) must be by far the
shortest, which often isn't the case here. Another demonstration of
this fact is given in \cite{Link2022Feb}, where Markovian dynamics are
this fact is given in \refcite{Link2022Feb}, where Markovian dynamics are
compared with the Redfield and exact dynamics for the spin-boson model
coupled to a squeezed bath. As in \cite{Xu2022Mar}, the Redfield
coupled to a squeezed bath. As in \refcite{Xu2022Mar}, the Redfield
description is found to be adequate for weak coupling. This is due to
the Redfield master equation not requiring the secular approximation,
but only weak coupling. It can therefore faithfully capture

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@ -1,7 +1,7 @@
\chapter{Conclusion and Ideas for future Work}
\label{cha:concl-ideas-future}
A worthwhile task for future work would be to verify the results
summarized in \cite{Binder2018} for the Otto cycle. Especially the
summarized in \refcite{Binder2018} for the Otto cycle. Especially the
optimization for optimal power which leads to the
NovikovCurzonAhlborn efficiency \(η_{ca}=1-\sqrt{T_{c}/T_{h}}\) is
interesting in the case of stronger coupling.
@ -13,10 +13,10 @@ studying the effect of overlapping and shifting strokes is a
fascinating avenue for future exploration.
Also, more interesting working media, such as a three level system are
of interest. In \cite{Uzdin2015Sep} it is shown, that in certain
of interest. In \refcite{Uzdin2015Sep} it is shown, that in certain
regimes quantum coherence can lead to superior power output. In the
same regime different types heat engines are equivalent. Both these
effects have been observed experimentally in \cite{Klatzow2019Mar}. It
effects have been observed experimentally in \refcite{Klatzow2019Mar}. It
would be interesting to see if the slight deviations from theory in
\cite{Klatzow2019Mar} could be explained using HOPS.
@ -30,9 +30,9 @@ consequence of the energy time uncertainty it is being argued, that
the origin of this advantage is truly quantum. The tools for the
exploitation of this effect and its verification are provided in this
work. However, a strong coupling analysis has already been performed
using HEOM in \cite{Xu2022Mar}.
using HEOM in \refcite{Xu2022Mar}.
In \cite{Santos2021Jun} a cycle is proposed that first creates states
In \refcite{Santos2021Jun} a cycle is proposed that first creates states
of finite ergotropy by letting energy flow through the working medium
and then extracting this ergotropy in a separate stroke. This work
could be verified and expanded to the non-Markovian regime.

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@ -96,7 +96,7 @@ passive iff the maximizing \(U\) \cref{eq:ergo_def} is the identity
\(\id\). In other words, a state is passive if its energy can not be
reduced through unitary transformations and its ergotropy vanishes.
In \cite{Niedenzu2018Jan} the ergotropy of the system is employed for
In \refcite{Niedenzu2018Jan} the ergotropy of the system is employed for
the definition of heat to derive a tighter second law. The immediate
appeal of this quantity for the purposes of this work however is its
to the full unitary dynamics of system \emph{and} bath which is
@ -813,7 +813,7 @@ relaxed, as \cref{eq:secondlaw_cyclic} holds as soon as
\(ΔS_\sys^\cyc\) vanishes.
The left hand side could be called ``bath entropy production'' as is
motivated in \cite{Riechers2021Apr}, where heat is identified with
motivated in \refcite{Riechers2021Apr}, where heat is identified with
\(ΔE_{\bath^i}\). There, the entropy production bound
\cref{eq:bathenergyandsystementro} that takes into account system and
bath is being considered and brought into connection with
@ -892,7 +892,7 @@ densities have been shifted such that their maxima coincide with
\(1 + Δ\) which relates to \cref{sec:energy-transf-char}. The
resonance criterion for modulated systems is derived from Floquet
theory~\cite{Kurizki2021Dec} which once again is a weak coupling
result, that carries over to other regimes. In \cite{Xu2022Mar} it is
result, that carries over to other regimes. In \refcite{Xu2022Mar} it is
shown, that for stronger coupling the situation is more complicated
but that, just like in \cref{sec:energy-transf-char}, the resonance
criterion is still a good starting point.