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\begin{document}
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\begin{center}
  \Large
  Calculating Energy Flows in Strongly Coupled Open Quantum Systems with
  HOPS
  \vspace{16pt}
  % Author names and affiliations
  \small \underline{Valentin Boettcher}$^1$, Richard Hartmann$^1$,
  Konstantin Beyer$^1$, Walter Strunz$^1$
  \\
  $^1$ Institute for Theoretical Physics, Dresden, Germany\\
  E-mail: \texttt{valentin.boettcher@tu-dresden.de}\\
  \vspace{8pt}
\end{center}
\normalsize
The hierarchy of pure states
(HOPS~\cite{Hartmann2017Dec,Diosi1998Mar}) is a general purpose
stochastic numerical framework for the exact simulation of
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 \refcite{Kato2016Dec}
for the Hierarchical Equations Of Motion method to arbitrary
modulations of system and coupling inheriting all the advantages of
the HOPS method.

We present the basic theory and its application to simple driven
spin-boson like systems, as well as a comparison with an exact
solution for a quantum Brownian motion like model.
\begin{figure}[H]
  \centering
  \subcaptionbox{Comparison of the bath energy change \(J_i=-∂_t\ev{H_{B,i}}\)
    for two harmonic oscillators coupled to two
    baths and each other.}{\input{./figs/poster_abstract/flow_comp.pgf}}
  \subcaptionbox{Total energy and interaction energy for a qubit
    coupled to a bath with long correlation time under fast
    modulation.}
  {\input{./figs/poster_abstract/energy_shovel_preview.pgf}}
\end{figure}
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