Phenomenological memory-kernel master equations and time-dependent Markovian processes

TL;DR

This paper challenges the assumption that memory kernel master equations inherently describe non-Markovian quantum dynamics, showing through examples that they can also represent time-dependent Markovian processes with unidirectional information flow.

Contribution

It demonstrates that phenomenological memory kernel master equations do not necessarily imply non-Markovian behavior, clarifying their interpretation in quantum dynamics.

Findings

Memory kernel equations can describe Markovian processes.

No reverse information flow in the considered equations.

Memory effects do not always indicate non-Markovianity.

Abstract

Do phenomenological master equations with memory kernel always describe a non-Markovian quantum dynamics characterized by reverse flow of information? Is the integration over the past states of the system an unmistakable signature of non-Markovianity? We show by a counterexample that this is not always the case. We consider two commonly used phenomenological integro-differential master equations describing the dynamics of a spin 1/2 in a thermal bath. By using a recently introduced measure to quantify non-Markovianity [H.-P. Breuer, E.-M. Laine, and J. Piilo, Phys. Rev. Lett. 103, 210401 (2009)] we demonstrate that as far as the equations retain their physical sense, the key feature of non-Markovian behavior does not appear in the considered memory kernel master equations. Namely, there is no reverse flow of information from the environment to the open system. Therefore, the assumption that the integration over a memory kernel always leads to a non-Markovian dynamics turns out to be vulnerable to phenomenological approximations. Instead, the considered phenomenological equations are able to describe time-dependent and uni-directional information flow from the system to the reservoir associated to time-dependent Markovian processes.