On the derivation of the GKLS equation for weakly coupled systems

TL;DR

This paper rigorously derives a GKLS master equation for a small quantum system interacting with a generic, non-thermal reservoir that has a mixing property, broadening the applicability of weak-coupling quantum dynamics models.

Contribution

It provides a novel derivation of the GKLS equation without assuming bosonic, fermionic, or thermal nature of the bath, relying instead on a clustering property of the reservoir.

Findings

Derived a GKLS master equation for generic baths

Extended the derivation beyond bosonic/fermionic/thermal assumptions

Identified the importance of the reservoir's mixing property

Abstract

We consider the reduced dynamics of a small quantum system in interaction with a reservoir when the initial state is factorized. We present a rigorous derivation of a GKLS master equation in the weak-coupling limit for a generic bath, which is not assumed to have a bosonic or fermionic nature, and whose reference state is not necessarily thermal. The crucial assumption is a reservoir state endowed with a mixing property: the n-point connected correlation function of the interaction must be asymptotically bounded by the product of two-point functions (clustering property).