Class of exact memory-kernel master equations

TL;DR

This paper introduces a class of bipartite Lindblad-type master equations that allow for exact, closed-form reduced dynamics of a quantum system coupled to an auxiliary, with detailed derivations via collision models.

Contribution

It identifies a new class of exact memory-kernel master equations enabling precise reduced dynamics derivation for open quantum systems.

Findings

Exact reduced master equations derived for specific bipartite Lindblad models

Closed-form solutions valid for any initial product state

Microscopic derivation via collision model mapping

Abstract

A well-known situation in which a non-Markovian dynamics of an open quantum system $S$ arises is when this is coherently coupled to an auxiliary system $M$ in contact with a Markovian bath. In such cases, while the joint dynamics of $S$-$M$ is Markovian and obeys a standard (bipartite) Lindblad-type master equation (ME), this is in general not true for the reduced dynamics of $S$. Furthermore, there are several instances (\eg the dissipative Jaynes-Cummings model) in which a {\it closed} ME for the $S$'s state {\it cannot} even be worked out. Here, we find a class of bipartite Lindblad-type MEs such that the reduced ME of $S$ can be derived exactly and in a closed form for any initial product state of $S$-$M$. We provide a detailed microscopic derivation of our result in terms of a mapping between two collision models