Interplay of different environments in open quantum systems: Breakdown of the additive approximation

TL;DR

This paper investigates how multiple environments affect open quantum systems, specifically examining when the combined effects of dephasing and decay baths can be approximated additively in the quantum master equation.

Contribution

It identifies conditions under which the additive approximation of multiple baths in the master equation remains valid, linking it to the relative strength of dephasing and bath bandwidth.

Findings

Additivity holds when dephasing strength is small compared to bath bandwidth.

Effective non-Hermitian Hamiltonian describes the system under additive approximation.

The study clarifies the regimes where the additive approximation breaks down.

Abstract

We analyze an open quantum system under the influence of more than one environment: a dephasing bath and a probability-absorbing bath that represents a decay channel, as encountered in many models of quantum networks. In our case, dephasing is modeled by random fluctuations of the site energies, while the absorbing bath is modeled with an external lead attached to the system. We analyze under which conditions the effects of the two baths can enter additively the quantum master equation. When such additivity is legitimate, the reduced master equation corresponds to the evolution generated by an effective non-Hermitian Hamiltonian and a Haken-Strobl dephasing super-operator. We find that the additive decomposition is a good approximation when the strength of dephasing is small compared to the bandwidth of the probability-absorbing bath.