Open quantum systems coupled to finite baths: A hierarchy of master equations

TL;DR

This paper develops a hierarchy of master equations to accurately describe the dynamics of open quantum systems coupled to finite baths, extending traditional models to include bath evolution and imperfect measurements.

Contribution

It introduces a novel hierarchy of master equations that incorporate finite bath dynamics and measurement imperfections, improving upon traditional approaches.

Findings

Hierarchy improves accuracy with more bath information

Framework applies even with imperfect bath measurements

Application to central spin model demonstrates effectiveness

Abstract

An open quantum system in contact with an infinite bath approaches equilibrium, while the state of the bath remains unchanged. If the bath is finite, the open system still relaxes to equilibrium, but it induces a dynamical evolution of the bath state. In this work, we study the dynamics of open quantum systems in contact with finite baths. We obtain a hierarchy of master equations that improve their accuracy by including more dynamical information of the bath. For instance, as the least accurate but simplest description in the hierarchy we obtain the conventional Born-Markov-secular master equation. Remarkably, our framework works even if the measurements of the bath energy are imperfect, which, not only is more realistic, but also unifies the theoretical description. Also, we discuss this formalism in detail for a particular non-interacting environment where the Boltzmann temperature and the Kubo-Martin-Schwinger relation naturally arise. Finally, we apply our hierarchy of master equations to study the central spin model.