Initial Correlations in Open Quantum Systems: Constructing Linear
Dynamical Maps and Master Equations
- URL: http://arxiv.org/abs/2210.13241v1
- Date: Mon, 24 Oct 2022 13:43:04 GMT
- Title: Initial Correlations in Open Quantum Systems: Constructing Linear
Dynamical Maps and Master Equations
- Authors: Alessandra Colla, Niklas Neubrand and Heinz-Peter Breuer
- Abstract summary: We show that, for any predetermined initial correlations, one can introduce a linear dynamical map on the space of operators of the open system.
We demonstrate that this construction leads to a linear, time-local quantum master equation with generalized Lindblad structure.
- Score: 62.997667081978825
- License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
- Abstract: We investigate the dynamics of open quantum systems which are initially
correlated with their environment. The strategy of our approach is to analyze
how given, fixed initial correlations modify the evolution of the open system
with respect to the corresponding uncorrelated dynamical behavior with the same
fixed initial environmental state, described by a completely positive dynamical
map. We show that, for any predetermined initial correlations, one can
introduce a linear dynamical map on the space of operators of the open system
which acts like the proper dynamical map on the set of physical states and
represents its unique linear extension. Furthermore, we demonstrate that this
construction leads to a linear, time-local quantum master equation with
generalized Lindblad structure involving time-dependent, possibly negative
transition rates. Thus, the general non-Markovian dynamics of an open quantum
system can be described by means of a time-local master equation even in the
case of arbitrary, fixed initial system-environment correlations. We present
some illustrative examples and explain the relation of our approach to several
other approaches proposed in the literature.
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