Structure of completely positive quantum master equations with memory kernel

TL;DR

This paper extends semi-Markov processes to quantum systems, deriving master equations with memory kernels that ensure complete positivity, thereby advancing the understanding of non-Markovian quantum dynamics.

Contribution

It introduces a framework for quantum semi-Markov processes with explicit conditions for complete positivity, enriching the structural understanding of non-Markovian open quantum system dynamics.

Findings

Derived quantum master equations with memory kernels

Established conditions for complete positivity of quantum maps

Analyzed explicit examples of non-Markovian dynamics

Abstract

Semi-Markov processes represent a well known and widely used class of random processes in classical probability theory. Here, we develop an extension of this type of non-Markovian dynamics to the quantum regime. This extension is demonstrated to yield quantum master equations with memory kernels which allow the formulation of explicit conditions for the complete positivity of the corresponding quantum dynamical maps, thus leading to important insights into the structural characterization of the non-Markovian quantum dynamics of open systems. Explicit examples are analyzed in detail.