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

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.

12 pages, 3 figures

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• Local and global approaches to the thermodynamics of pure decoherence processes in open quantum systems
• Unveiling coherent dynamics in non-Markovian open quantum systems: exact expression and recursive perturbation expansion
• Recursive perturbation approach to time-convolutionless master equations: Explicit construction of generalized Lindblad generators for arbitrary open systems
• Dynamics of Open Quantum Systems with Initial System-Environment Correlations via Stochastic Unravelings
• Verifying Quantum Memory in the Dynamics of Spin Boson Models
• Limitations of the Markovian approximation in the harmonic oscillator
• Anomalous flow in correlated quantum systems: No-go result and multiple-charge scenario
• On the distinction between distinguishability of states and witness of non-Markovianity of dynamical maps
• Towards kinetic equations of open systems of active soft matter