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add future projects and kill anti-zeno

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28
references.bib
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@ -1402,3 +1402,31 @@
address = {Singapore},
url = {https://books.google.de/books/about/Quantum_Dissipative_Systems.html?id=S2K6CgAAQBAJ&redir_esc=y}
}
@article{Xu2022Mar,
author = {Xu, Meng and Stockburger, J. T. and Kurizki, G. and Ankerhold, J.},
title = {{Minimal quantum thermal machine in a bandgap environment: non-Markovian features and anti-Zeno advantage}},
journal = {New J. Phys.},
volume = {24},
number = {3},
pages = {035003},
year = {2022},
month = mar,
issn = {1367-2630},
publisher = {IOP Publishing},
doi = {10.1088/1367-2630/ac575b}
}
@article{Shi2009Feb,
author = {Shi, Qiang and Chen, Liping and Nan, Guangjun and Xu, Rui-Xue and Yan, YiJing},
title = {{Efficient hierarchical Liouville space propagator to quantum dissipative dynamics}},
journal = {J. Chem. Phys.},
volume = {130},
number = {8},
pages = {084105},
year = {2009},
month = feb,
issn = {0021-9606},
publisher = {American Institute of Physics},
doi = {10.1063/1.3077918}
}

17
src/hops_tweak.tex
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@ -2,8 +2,10 @@
\label{chap:hops_notes}
\section{Normalized HOPS}%
\label{sec:norm}
In this short note we introduce a \emph{stable} norm preserving term
into the HOPS equations.
We introduce full HOPS vector \(Ψ = \qty(ψ, φ)\) which can be
We introduce the full HOPS vector \(Ψ = \qty(ψ, φ)\) which can be
decomposed into the zeroth hierarchy order state \(ψ\) and the
non-zero order states \(φ\).
@ -318,14 +320,14 @@ magnitude can be estimated as follows
\norm{L} \sum_{μ=1}^M \frac{\abs{G_μ}}{\Re[W_μ]}.
\end{equation}
It is unclear how this shift should be treated. Simply adding it to
the denominator of~\cref{eq:steadynorm} lead to a breakdown of the
the denominator of~\cref{eq:steadynorm} leads to a breakdown of the
bound for numerical testing. A better estimate should account for
this and also for the coupling to the lower orders foregoing the
recursive nature of the estimate.
The relation \cref{eq:steadynorm} is recursive
and break off at \(ψ^0\), the norm of which can be assumed to be unity
in the nonlinear method.
The relation \cref{eq:steadynorm} is recursive and breaks off at
\(ψ^0\), the norm of which can be assumed to be unity in the nonlinear
method.
These ideas remain to be verified. Especially the assumptions should
be checked. For time dependent coupling, one may maximize the estimate
@ -371,7 +373,10 @@ Calculating \(M_{\vb{k}}\) explicitly and demanding it to be small
truncation scheme below a certain coupling strength.
Some basic experimentation has shown, that the cutoff parameter has to
be tuned and is not universally valid which is in accord with the
findings of \cite{RichardDiss}.
findings of~\cite{RichardDiss}.
Similarly to~\cite{Shi2009Feb}, a dynamic truncation scheme could also
be implemented.
\section{Some Mathematical Details}
\label{math_detail}

99
src/thermo.tex
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@ -1201,7 +1201,7 @@ Here, we consider a spin boson model much like the one in
The modulation functions \(f\) and \(h_{i}\) are periodic and
constructed out of smoothstep\footnote{see \cref{sec:smoothstep}}
functions. Rather than giving the precise formulas, we instead plot
functions similar to \cite{Wiedmann2021Jun}. Rather than giving the precise formulas, we instead plot
all the modulations over one period in \cref{fig:ottomod}.
\begin{figure}[htp]
\centering
@ -1253,10 +1253,10 @@ to the total power is the system. The narrowing stroke produces
negative (usable) power and the widening produces positive power that
has to be supplied externally. More importantly however, we find that
also the modulation of the interaction, i.e. the coupling and
decoupling produce predominantly positive power that reduces the energy
output. In a weak
coupling scheme, this contribution can be neglected. Not so however in
the generic case presented here.
decoupling produce predominantly positive power that 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 arrived at in \cite{Wiedmann2021Jun}.
The mean power output of this cycle is
\(\bar{P}=0.002468\pm 0.000021\) with an efficiency, as defined in
@ -1342,6 +1342,18 @@ Nevertheless, if the cycle was very fast, the effect of the
continuously coupled version of the cycle is superior. See also the
remarks below about \cite{Uzdin2015Sep}.
% \section{Anti Zeno Engine}
% \label{sec:antizeno}
% \begin{itemize}
% \item mention concept
% \item results not reliable in time for thesis
% \item interesting because: non markovian QUANTUM advantage. a bit
% sensational ;P
% \end{itemize}
\section{Some Proposals for future Work}
\label{sec:some-prop-future}
A worthwhile task for future work would be to verify the results
summarized in \cite{Binder2018} for the Otto cycle. Especially the
optimization for optimal power which leads to the
@ -1362,42 +1374,47 @@ effects have been observed experimentally in \cite{Klatzow2019Mar}. It
would be interesting to see if the slight deviations from theory in
\cite{Klatzow2019Mar} could be explained using HOPS.
\section{Anti Zeno Engine}
\label{sec:antizeno}
\begin{itemize}
\item mention concept
\item results not reliable in time for thesis
\item interesting because: non markovian QUANTUM advantage. a bit
sensational ;P
\end{itemize}
The so called Anti-Zeno Effect occurring in systems under fast
modulation has recently received some attention
\cite{Mukherjee2020Jan,Xu2022Mar}. An advantage is claimed to exist,
due to the broadening of the resonance criterion which we have
observed in
\cref{sec:one_bath_cutoff,sec:modcoup_reso,sec:otto}. Being a
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}.
\section{Some Proposals for future Work}
\begin{itemize}
\item a list of ideas and some papers I've came across
\item projects for future theses or papers
\end{itemize}
In \cite{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.
A useful improvement of the method would be the ability to snapshot
the total state of system and bath and then propagate this state with
different modulation protocols.
\begin{itemize}
\item ... list all those nice papers ...
\item the third law
\item look more deeply into the peculiarities in \cref{sec:oneosccomp}
\item verify speculation of energy flow vs non-markvianity: flow
between two baths though a system
\item three level system -> paper
\item driven spin boson -> paper \cite{Magazzu2018Apr}
\item flows crossing in one point: robust featureu
\item linear regeime of steady state energies -> universal, how far
does it extend
\item more detailed parameter scans, universality between different models?
\item state changes -> is energy difference = heat + work path
independent (maybe try different protocols and turn off interaction
at for beginning and end in an adiabatic way...)
\item compare with results from master equation in \cref{sec:prec_sim}
\item steady state methods, better convergence for long-time
simulations
\item coupling to single bath: although breach of second law forbidden
-> cyclical energy transfer for very long bath correlation times
\item filter mode: \cref{sec:shift_sp}
\item otto cycle: sensitivity to timing stronger with stronger coupling?
\end{itemize}
% \begin{itemize}
% \item ... list all those nice papers ...
% \item the third law
% \item look more deeply into the peculiarities in \cref{sec:oneosccomp}
% \item verify speculation of energy flow vs non-markvianity: flow
% between two baths though a system
% \item three level system -> paper
% \item driven spin boson -> paper \cite{Magazzu2018Apr}
% \item flows crossing in one point: robust featureu
% \item linear regeime of steady state energies -> universal, how far
% does it extend
% \item more detailed parameter scans, universality between different models?
% \item state changes -> is energy difference = heat + work path
% independent (maybe try different protocols and turn off interaction
% at for beginning and end in an adiabatic way...)
% \item compare with results from master equation in \cref{sec:prec_sim}
% \item steady state methods, better convergence for long-time
% simulations
% \item coupling to single bath: although breach of second law forbidden
% -> cyclical energy transfer for very long bath correlation times
% \item filter mode: \cref{sec:shift_sp}
% \item otto cycle: sensitivity to timing stronger with stronger coupling?
% \end{itemize}