Quantum Semi-Markov Processes

TL;DR

This paper introduces a broad class of non-Markovian quantum master equations based on quantum semi-Markov processes, enabling better modeling of systems with strong memory effects.

Contribution

It generalizes classical semi-Markov processes to quantum systems and establishes conditions for the complete positivity of the resulting dynamical maps.

Findings

Provides a framework for non-Markovian quantum dynamics with memory effects

Includes examples from quantum optics and transport models

Formulates conditions for physical validity of the processes

Abstract

We construct a large class of non-Markovian master equations that describe the dynamics of open quantum systems featuring strong memory effects, which relies on a quantum generalization of the concept of classical semi-Markov processes. General conditions for the complete positivity of the corresponding quantum dynamical maps are formulated. The resulting non-Markovian quantum processes allow the treatment of a variety of physical systems, as is illustrated by means of various examples and applications, including quantum optical systems and models of quantum transport.