Non-Markovianity of the Post Markovian Master Equation

TL;DR

This paper reviews the Post-Markovian master equation, demonstrating its ability to model non-Markovian quantum dynamics through explicit examples and mathematical conditions on the memory kernel.

Contribution

It provides a solvable framework for non-Markovian quantum dynamics and establishes conditions for non-CP-divisible evolution within this model.

Findings

Solutions exhibit non-Markovianity using distinguishability measures

Explicit analysis of quantum dynamical map divisibility

Mathematical condition for non-CP-divisible dynamics

Abstract

An easily solvable quantum master equation has long been sought that takes into account memory effects induced on the system by the bath, i.e., non-Markovian effects. We briefly review the Post-Markovian master equation (PMME), which is relatively easy to solve, and analyze a simple example where solutions obtained exhibit non-Markovianity. We apply the distinguishability measure introduced by Breuer et al., and we also explicitly analyze the divisibility of the associated quantum dynamical maps. We give a mathematical condition on the memory kernel used in the PMME that guarantees non-CP-divisible dynamics.