mirror of
https://github.com/vale981/master-thesis-tex
synced 2025-03-05 09:31:39 -05:00
fix "in refs...."
This commit is contained in:
parent
bfa9f883b8
commit
af31fc054d
7 changed files with 40 additions and 14 deletions
|
@ -82,4 +82,30 @@ linkcolor=blue,
|
||||||
% cursive bold in maths
|
% cursive bold in maths
|
||||||
\unimathsetup{math-style=TeX,bold-style=ISO}
|
\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
|
\recalctypearea
|
||||||
|
|
|
@ -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
|
For completeness, it may be of interest to find a solution for
|
||||||
negative times. This solution is relatively unphysical, as the initial
|
negative times. This solution is relatively unphysical, as the initial
|
||||||
condition of a product state\footnote{For a treatment of more general
|
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
|
open system dynamics~\cite{Rivas2012}. Therefore a system that starts
|
||||||
out in some entangled state just to reach the perfect product state at
|
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
|
\(t=0\) is not something that is likely to be applicable to physical
|
||||||
|
|
|
@ -518,7 +518,7 @@ through energy conservation as in~\cite{Kato2016Dec}, we find
|
||||||
H_\inter^{(n)}]}
|
H_\inter^{(n)}]}
|
||||||
\end{equation}
|
\end{equation}
|
||||||
regardless of the (non-) commutativity\footnote{For example, the
|
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
|
non-commuting couplings.} of the interaction
|
||||||
Hamiltonians. Therefore, we can apply the formalism of the previous
|
Hamiltonians. Therefore, we can apply the formalism of the previous
|
||||||
sections almost unchanged, by taking care that all quantities involved
|
sections almost unchanged, by taking care that all quantities involved
|
||||||
|
|
|
@ -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}.
|
-\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}
|
\end{equation}
|
||||||
There is a subtlety concerning the functional derivative that won't be
|
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
|
\cref{sec:nonlin_flow}. Crucially, the system state is now recovered
|
||||||
through
|
through
|
||||||
\begin{equation}
|
\begin{equation}
|
||||||
|
|
|
@ -1443,7 +1443,7 @@ with specific bath degrees of freedom which are independent themselves
|
||||||
except for their interaction with the system.
|
except for their interaction with the system.
|
||||||
|
|
||||||
This interpretation is corroborated by a time discrete version of the
|
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
|
\emph{Time-Oscillator picture} is introduced, which shows that a
|
||||||
variant of the NMQSD can be formulated as the successive interaction
|
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
|
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
|
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
|
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
|
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
|
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
|
description is found to be adequate for weak coupling. This is due to
|
||||||
the Redfield master equation not requiring the secular approximation,
|
the Redfield master equation not requiring the secular approximation,
|
||||||
but only weak coupling. It can therefore faithfully capture
|
but only weak coupling. It can therefore faithfully capture
|
||||||
|
|
|
@ -1,7 +1,7 @@
|
||||||
\chapter{Conclusion and Ideas for future Work}
|
\chapter{Conclusion and Ideas for future Work}
|
||||||
\label{cha:concl-ideas-future}
|
\label{cha:concl-ideas-future}
|
||||||
A worthwhile task for future work would be to verify the results
|
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
|
optimization for optimal power which leads to the
|
||||||
Novikov–Curzon–Ahlborn efficiency \(η_{ca}=1-\sqrt{T_{c}/T_{h}}\) is
|
Novikov–Curzon–Ahlborn efficiency \(η_{ca}=1-\sqrt{T_{c}/T_{h}}\) is
|
||||||
interesting in the case of stronger coupling.
|
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.
|
fascinating avenue for future exploration.
|
||||||
|
|
||||||
Also, more interesting working media, such as a three level system are
|
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
|
regimes quantum coherence can lead to superior power output. In the
|
||||||
same regime different types heat engines are equivalent. Both these
|
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
|
would be interesting to see if the slight deviations from theory in
|
||||||
\cite{Klatzow2019Mar} could be explained using HOPS.
|
\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
|
the origin of this advantage is truly quantum. The tools for the
|
||||||
exploitation of this effect and its verification are provided in this
|
exploitation of this effect and its verification are provided in this
|
||||||
work. However, a strong coupling analysis has already been performed
|
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
|
of finite ergotropy by letting energy flow through the working medium
|
||||||
and then extracting this ergotropy in a separate stroke. This work
|
and then extracting this ergotropy in a separate stroke. This work
|
||||||
could be verified and expanded to the non-Markovian regime.
|
could be verified and expanded to the non-Markovian regime.
|
||||||
|
|
|
@ -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
|
\(\id\). In other words, a state is passive if its energy can not be
|
||||||
reduced through unitary transformations and its ergotropy vanishes.
|
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
|
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
|
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
|
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.
|
\(ΔS_\sys^\cyc\) vanishes.
|
||||||
|
|
||||||
The left hand side could be called ``bath entropy production'' as is
|
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
|
\(ΔE_{\bath^i}\). There, the entropy production bound
|
||||||
\cref{eq:bathenergyandsystementro} that takes into account system and
|
\cref{eq:bathenergyandsystementro} that takes into account system and
|
||||||
bath is being considered and brought into connection with
|
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
|
\(1 + Δ\) which relates to \cref{sec:energy-transf-char}. The
|
||||||
resonance criterion for modulated systems is derived from Floquet
|
resonance criterion for modulated systems is derived from Floquet
|
||||||
theory~\cite{Kurizki2021Dec} which once again is a weak coupling
|
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
|
shown, that for stronger coupling the situation is more complicated
|
||||||
but that, just like in \cref{sec:energy-transf-char}, the resonance
|
but that, just like in \cref{sec:energy-transf-char}, the resonance
|
||||||
criterion is still a good starting point.
|
criterion is still a good starting point.
|
||||||
|
|
Loading…
Add table
Reference in a new issue