Initial Correlations in Open Quantum Systems: Constructing Linear Dynamical Maps and Master Equations

TL;DR

This paper develops a framework for describing the dynamics of open quantum systems with initial correlations using linear dynamical maps and time-local master equations, extending the understanding of non-Markovian quantum evolution.

Contribution

It introduces a method to construct a unique linear dynamical map and a time-local master equation for systems with initial correlations, generalizing previous models.

Findings

Linear dynamical maps can be constructed for correlated initial states.

Time-local master equations with generalized Lindblad form are applicable.

The approach captures non-Markovian dynamics with initial correlations.

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.