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Valentin Boettcher 2022-09-27 19:33:49 +02:00
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@ -801,11 +801,11 @@ to be useful. Assume that the interaction Hamiltonian in
system and bath energy expectation values can be cleanly separated. In
the periodic steady state the system energy does not change after a
cycle and the whole energy change amounts to the change in bath
energies. The energy changes in the individual baths are then well
defined and useful (macroscopic) quantities, whether one calls them
heat or not. In a setting with two baths \cref{eq:secondlaw_cyclic}
implies the Carnot bound for the efficiency given in
\cref{eq:efficiency_definition}.
energies. The energy changes in the individual baths are then
well-defined and useful (macroscopic) quantities, whether one calls
them heat or not. In a setting with two baths
\cref{eq:secondlaw_cyclic} implies the Carnot bound for the efficiency
given in \cref{eq:efficiency_definition}.
Let us now proceed to simulations of systems to which the
considerations of \cref{sec:basic_thermo} are applicable. This will
@ -824,12 +824,11 @@ found in \cref{sec:ergoonebath} that this also holds for a finite
quantum system coupled to a thermal bath. In \cref{sec:explicitergo}
we found, that the bound given on the ergotropy in such a situation
can be saturated for infinite baths, such as the ones used with
NMQSD/HOPS. However, it is unclear if such a unitary transformation
can be implemented without explicit construction of a model. Our goal
in this section is to extract as much energy from a one-bath system as
is possible without extensive tuning. We will applying the results of
the previous studies of \cref{chap:numres} to produce consistent
results.
NMQSD/HOPS. However, it is unclear how such a unitary transformation
can be implemented concretely. Our goal in this section is to extract
as much energy from a one-bath system as is possible without extensive
tuning. We will be applying the results of the previous studies of
\cref{chap:numres} to produce consistent results.
In this section we will focus on the minimal dimensionless model of a
qubit interacting with a bath in a spin-boson like manner, however
@ -847,10 +846,13 @@ are scaling with \(λ\). For \(λ=0\) the system Hamiltonian is positive
semi-definite with the energies zero and one. The modulation of the
interaction has been chosen heuristically to always act in the same
``direction'' and vanish periodically. The last fact is important, as
we will be interested in the behavior of the system before it has
we will be interested in the behaviour of the system before it has
reached the steady state. The energy extracted from a system should be
gauged in such a way, that an additional decoupling is not necessary.
The goal is now to extract as much energy as possible from the total
system.
We choose the ``down state'' with \(H(0)\ket{0}=0\) as initial state,
as we want to extract energy from the bath and not the system. To
maximize the energy flow, we will use resonant baths whose spectral