On the conundrum of deriving exact solutions from approximate master equations

TL;DR

This paper derives the exact time-evolution for quantum systems under phase-noise and shows that a second-order perturbative master equation can yield exact results for Gaussian initial bath states, clarifying its relation to the Bloch-Redfield approach.

Contribution

It demonstrates the conditions under which a second-order time-local master equation provides exact solutions for quantum systems with phase-noise, linking it to Gaussian bath states and the Bloch-Redfield method.

Findings

Exact evolution derived for phase-noise systems.

Second-order master equation matches exact results for Gaussian baths.

Clarifies the relation to Bloch-Redfield approach.

Abstract

We derive the exact time-evolution for a general quantum system under the influence of pure phase-noise and demonstrate that for a Gaussian initial state of the bath, the exact result can be obtained also within a perturbative time-local master equation approach already in second order of the system-bath coupling strength. We reveal that this equivalence holds if the initial state of the bath can be mapped to a Gaussian phase-space distribution function. Moreover, we discuss the relation to the standard Bloch-Redfield approach.