Quantum Trajectories in Random Environment: the Statistical Model for a Heat Bath

TL;DR

This paper derives stochastic master equations for a quantum system in a heat bath, modeling continuous measurements and providing a physically interpretable framework based on photon emissions and absorptions.

Contribution

It introduces a new statistical model for a heat bath that differs from previous Gibbs models, with rigorous derivation via martingale problems.

Findings

Derived stochastic master equations for quantum systems in heat baths.

Provided a physical interpretation in terms of photon emissions and absorptions.

Established models of random environments and their unravelings.

Abstract

In this article, we derive the stochastic master equations corresponding to the statistical model of a heat bath. These stochastic differential equations are obtained as continuous time limits of discrete models of quantum repeated measurements. Physically, they describe the evolution of a small system in contact with a heat bath undergoing continuous measurement. The equations obtained in the present work are qualitatively different from the ones derived in \cite{A1P1}, where the Gibbs model of heat bath has been studied. It is shown that the statistical model of a heat bath provides clear physical interpretation in terms of emissions and absorptions of photons. Our approach yields models of random environment and unravelings of stochastic master equations. The equations are rigorously obtained as solutions of martingale problems using the convergence of Markov generators.