Markovian quantum master equations are exponentially accurate in the weak coupling regime

TL;DR

This paper proves that Markovian quantum master equations accurately describe open quantum systems coupled to Gaussian environments at weak coupling, with errors decreasing exponentially as the coupling weakens, supported by explicit formulas and numerical benchmarks.

Contribution

It provides a rigorous derivation and bounds for Markovian quantum master equations in the weak coupling regime, showing exponential suppression of non-Markovian effects.

Findings

Error bounds decrease exponentially with inverse coupling strength

Explicit expression for the Markovian quantum master equation

Numerical validation on an exactly solvable model

Abstract

We consider the evolution of open quantum systems coupled to one or more Gaussian environments. We demonstrate that such systems can be described by a Markovian quantum master equation (MQME) up to a correction that decreases exponentially with the inverse system-bath coupling strength. We provide an explicit expression for this MQME, along with rigorous bounds on its residual correction, and numerically benchmark it for an exactly solvable model. The MQME is obtained via a generalized Born-Markov approximation that can be iterated to arbitrary orders in the system-bath coupling; our error bound converges asymptotically to zero with the iteration order. Our results thus demonstrate that the non-Markovian component in the evolution of an open quantum system, while possibly inevitable, can be exponentially suppressed at weak coupling.