more typo

This commit is contained in:
Valentin Boettcher 2022-09-27 16:19:09 +02:00
parent a7356c063b
commit d6ad82e2af
No known key found for this signature in database
GPG key ID: E034E12B7AF56ACE
8 changed files with 42 additions and 43 deletions

View file

@ -93,7 +93,7 @@
\def\hilb{\ensuremath{\mathcal{H}}}
% fixme
\newcommand{\fixme}[1]{\marginpar{\tiny\textcolor{red}{#1}}}
\newcommand{\fixme}[1]{} %{\marginpar{\tiny\textcolor{red}{#1}}}
% HOPS/NMQSD
\def\sys{\ensuremath{\mathrm{S}}}
@ -140,3 +140,28 @@
\newcommand{\plot}[1]{%
\includegraphics[draft=false]{./figs/#1.pdf}}
\newcommand{\tval}[1]{{\input{./values/#1.tex}}}
%% 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}

View file

@ -82,30 +82,4 @@ 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

View file

@ -38,7 +38,7 @@ non-Markovian strongly coupled open systems. Without modification of
the core method, it is possible to calculate the interaction energy
and the bath energy change. This is due to HOPS' foundation on the
global dynamics of the system and the bath in contrast to
master-equation methods. We extended the result in~\cite{Kato2016Dec}
master-equation methods. We extended the result in \refcite{Kato2016Dec}
for the Hierarchical Equations Of Motion method to arbitrary
modulations of system and coupling inheriting all the advantages of
the HOPS method.

View file

@ -136,7 +136,7 @@ Defining
\label{eq:defdop}
D_t = ∫_0^t\dd{s} \alpha(t-s)\fdv{η^\ast_s}
\end{equation}
as in~\cite{Suess2014Oct} we find
as in \refcite{Suess2014Oct} we find
\begin{equation}
\label{eq:final_flow_nmqsd}
J(t) = -\i \mathcal{M}_{η^\ast}\bra{\psi(η,
@ -511,7 +511,7 @@ general. We refer to \cref{sec:hops_multibath} for an review of the
NMQSD theory and HOPS method for multiple baths.
Because the bath energy change is being calculated directly and not
through energy conservation as in~\cite{Kato2016Dec}, we find
through energy conservation as in \refcite{Kato2016Dec}, we find
\begin{equation}
\label{eq:general_n_flow}
J_n=-\dv{\ev{H_\bath^{(n)}}}{t} = \iu\ev{[H_\bath^{(n)},

View file

@ -319,7 +319,7 @@ arrive at an equation for \(\ket{ψ(t,\vb{z}^{\ast})}\)
From this point on there are multiple avenues open to us. We choose
the canonical one of \cite{Strunz2001Habil}, but there is also a
time-discrete derivation, that avoids functional derivatives,
in~\cite{Hartmann2021Aug}.
in \refcite{Hartmann2021Aug}.
We shift the perspective and define~\cite{RichardDiss,Strunz2001Habil}
\begin{equation}
@ -486,7 +486,7 @@ We call \cref{eq:singlehops} the \emph{Hierarchy of Pure States}
because each hierarchy state couples only to the hierarchy states one
level above and one level below. This is similar to the
\emph{Hierarchical Equations of Motion} (HEOM) approach used
in~\cite{Kato2016Dec}, but with the advantage of reducing the
in \refcite{Kato2016Dec}, but with the advantage of reducing the
dimensionality from \(\dim{\hilb_{\sys}}^{2}\) to
\(\dim{\hilb_{\sys}}\) by treating pure states instead of density
matrices.

View file

@ -109,7 +109,7 @@ the ``Markovianity'' of the bath.
The ohmic spectral density models an environment with a physical
energy spectrum that is bounded from below and allows the application
of the finite temperature method described in~\cite{RichardDiss} and
of the finite temperature method described in \refcite{RichardDiss} and
\cref{sec:lin_finite}. Also, \(J(0) = 0\) ensures that there is a
unique zero temperature state of the bath. In~\cite{Kolar2012Aug} it
is argued (under weak coupling assumptions), that \(J(ω)\approx ω^γ\)
@ -122,7 +122,7 @@ It may be remarked, that~\cref{eq:ohmic_bcf} does not correspond to a
simple sum of exponentials. As such it exercises the HOPS method and
serves as a model for a general bath correlation function. For use
with HOPS, a sum of exponentials must be fitted to the BCF. This has
been done in~\cite{RichardDiss,Hartmann2021Aug}. In
been done in \refcite{RichardDiss,Hartmann2021Aug}. In
\cref{sec:hopsvsanalyt} we will see, that this is indeed a valid
strategy for the application of \cref{chap:flow}.
@ -753,7 +753,7 @@ the stochastic process we chose the cutoff \(\abs{\vb{k}} \leq 4\)
(simplex truncation\footnote{see \cref{sec:hops_basics}}),
\(N=4.5 \cdot 10^5\) trajectories and an Ohmic BCF with \(α(0)=1.6\)
and \(ω_c=4\). The sampling method uses the ``Fast Fourier
Transform'' (FFT) as described in~\cite{RichardDiss}. As the system
Transform'' (FFT) as described in \refcite{RichardDiss}. As the system
Hilbert space dimension is small, a BCF expansion with seven terms was
employed~\cite{Hartmann2021Aug,RichardDiss}.
@ -855,7 +855,7 @@ convergence as is also demonstrated in
\subsection{Hierarchy Truncation}
\label{sec:trunc}
As the systematics of the truncation depth have already been studied
thoroughly in~\cite{RichardDiss,Hartmann2021Aug}, we will keep the
thoroughly in \refcite{RichardDiss,Hartmann2021Aug}, we will keep the
discussion short. We chose \(N=4.5 \cdot 10^5\) trajectories and an
Ohmic BCF with \(α(0)=0.8\) and \(ω_c=2\). Again, a BCF expansion with
seven terms has been used. The coupling strength has been chosen with

View file

@ -73,7 +73,7 @@ change over one cycle.
In \cref{sec:operational_thermo} a Gibbs like inequality for an
arbitrary number of baths is derived as a slight generalization of the
derivation in~\cite{Kato2016Dec}. The left hand side of this
derivation in \refcite{Kato2016Dec}. The left hand side of this
inequality can be associated with a thermodynamic cost that should be
minimized for optimal efficiency.
@ -112,7 +112,7 @@ where \(n<∞\) is the Hilbert space dimension. This condition is both
necessary and sufficient. Examples of passive states are the state of
the micro-canonical ensemble or Gibbs states. Gibbs states are further
distinguished by additional features described
in~\cite{Lenard1978Dec}, which can be connected to formulations of the
in \refcite{Lenard1978Dec}, which can be connected to formulations of the
zeroth and second laws of thermodynamics.
One of these properties is complete passivity. Completely passive
@ -289,7 +289,7 @@ bath properties except the temperature. It is therefore reasonable to
expected that it is also valid for an infinite bath.
Interestingly, a saturation of \cref{eq:thermo_ergo_bound} is achieved
in~\cite{Skrzypczyk2014Jun} with a continuous qubit
in \refcite{Skrzypczyk2014Jun} with a continuous qubit
bath. In~\cite{Lobejko2021Feb} a more generic argument is made in a
similar setting. Both propose concrete protocols within the bounds of
thermal operations and by considering explicit work reservoirs. In
@ -672,7 +672,7 @@ energy that can be extracted out of the system in relation to the
energy that is simply transferred between the baths.
An argument based on entropy may be made for the periodic steady state
as was shown in~\cite{Kato2016Dec} and is reproduced here with the
as was shown in \refcite{Kato2016Dec} and is reproduced here with the
slight generalization of multiple baths and modulated coupling. We
will find a Clausius like form of the second law. The left hand side
of this inequality can then be interpreted as thermodynamic cost of
@ -789,7 +789,7 @@ If one defines heat in this
way~\cite{Kato2016Dec,Riechers2021Apr,Strasberg2021Aug},
\cref{eq:secondlaw_cyclic} amounts to the Clausius inequality. The
definition of heat as bath energy change is corroborated
in~\cite{Esposito2015Dec} where it is shown, ableit for fermionic
in \refcite{Esposito2015Dec} where it is shown, ableit for fermionic
baths, that a definition of heat involving any nonzero fraction of the
interaction energy will lead to the internal energy (as defined by the
first law) not being an exact differential.
@ -1391,7 +1391,7 @@ however, we find that also the modulation of the interaction, i.e. the
coupling and decoupling, figures into the total power and reduces the
energy output. In a weak coupling scheme, this contribution can be
neglected. Not so however in the generic case presented here. A
similar result was found in~\cite{Wiedmann2021Jun}.
similar result was found in \refcite{Wiedmann2021Jun}.
The mean power output of this cycle is
\(\bar{P}=0.002468\pm 0.000021\) with an efficiency, as defined in

View file

@ -817,7 +817,7 @@ labelformat=brace, position=top]{subcaption}
\(J(ω) = π ∑_λ\abs{g_λ}^2δ(ω-ω_λ)\)).
\end{frame}
\begin{frame}{Fock-Space Embedding}
As in~\cite{Gao2021Sep} we can define
As in \refcite{Gao2021Sep} we can define
\begin{equation}
\label{eq:fockpsi}
\ket{Ψ} = \sum_\kmat\ket{\psi^\kmat}\otimes \ket{\kmat}