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

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

2009-08-19

arxiv.org/abs/0908.2754v1

Confluentes Mathematici 1, 2 (2009) 249-289

Physics

Quantum Physics

Scientific paper

10.1142/S1793744209000109

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.

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