Stochastic Master Equations in Thermal Environment

TL;DR

This paper derives stochastic master equations for open quantum systems in thermal environments, showing that at positive temperature, the evolution is described by pure diffusion equations, extending zero-temperature jump-diffusion models.

Contribution

It introduces a derivation of stochastic master equations at positive temperature, demonstrating the transition from jump-diffusion to pure diffusion dynamics in quantum systems.

Findings

At positive temperature, only pure diffusion equations are relevant.

The equations are derived as limits of a quantum repeated measurement model.

The work extends zero-temperature models to finite temperature environments.

Abstract

We derive the stochastic master equations which describe the evolution of open quantum systems in contact with a heat bath and undergoing indirect measurements. These equations are obtained as a limit of a quantum repeated measurement model where we consider a small system in contact with an infinite chain at positive temperature. At zero temperature it is well-known that one obtains stochastic differential equations of jump-diffusion type. At strictly positive temperature, we show that only pure diffusion type equations are relevant.