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arXiv:1611.01150 · Physical Review Letters

Generalized Master Equations Leading to Completely Positive Dynamics

Bassano Vacchini

Published Nov 30, 2016• 74 citations

Abstract

We provide a general construction of quantum generalized master equations with a memory kernel leading to well-defined, that is, completely positive and trace-preserving, time evolutions. The approach builds on an operator generalization of memory kernels appearing in the description of non-Markovian classical processes and puts into evidence the nonuniqueness of the relationship arising due to the typical quantum issue of operator ordering. The approach provides a physical interpretation of the structure of the kernels, and its connection with the classical viewpoint allows for a trajectory description of the dynamics. Previous apparently unrelated results are now connected in a unified framework, which further allows us to phenomenologically construct a large class of non-Markovian evolutions taking as the starting point collections of time-dependent maps and instantaneous transformations describing the microscopic interaction dynamics.

DOI: 10.1103/physrevlett.117.230401

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