Non-divisiblity and non-Markovianity in a Gaussian dissipative dynamics

TL;DR

This paper investigates Gaussian dissipative dynamics through a stochastic Schrödinger equation, analyzing two definitions of non-Markovianity and revealing cases of their divergence.

Contribution

It introduces a model that allows detailed comparison of non-Markovianity definitions based on generator dependence and map divisibility.

Findings

Identifies cases with non-Markovianity in both senses.

Shows instances where one definition indicates non-Markovianity while the other does not.

Provides insights into the relationship between different non-Markovianity measures.

Abstract

We study a stochastic Schroedinger equation that generates a family of Gaussian dynamical maps in one dimension permitting a detailed exam of two different definitions of non-Markovianity: one related to the explicit dependence of the generator on the starting time, the other to the non-divisibility of the time-evolution maps. The model shows instances where one has non-Markovianity in both senses and cases when one has Markovianity in the second sense but not in the first one.