Evolution equations for quantum semi-Markov dynamics

TL;DR

This paper explores the relationship between local and non-local descriptions of quantum semi-Markov processes, providing insights into their master equations, non-Markovian features, and Markovian approximations.

Contribution

It introduces a new connection between local and non-local descriptions of quantum semi-Markov dynamics and analyzes the emergence of dephasing and Markovian approximations.

Findings

Coherent relationship established between local and non-local descriptions.

Dephasing terms emerge when transitioning between master equations.

Markovian approximation always valid for the studied class of dynamics.

Abstract

Using a newly introduced connection between the local and non-local description of open quantum system dynamics, we investigate the relationship between these two characterisations in the case of quantum semi-Markov processes. This class of quantum evolutions, which is a direct generalisation of the corresponding classical concept, guarantees mathematically well-defined master equations, while accounting for a wide range of phenomena, possibly in the non-Markovian regime. In particular, we analyse the emergence of a dephasing term when moving from one type of master equation to the other, by means of several examples. We also investigate the corresponding Redfield-like approximated dynamics, which are obtained after a coarse graining in time. Relying on general properties of the associated classical random process, we conclude that such an approximation always leads to a Markovian evolution for the considered class of dynamics.