QUANTUM TRAJECTORIES IN RANDOM ENVIRONMENT: THE STATISTICAL MODEL FOR A HEAT BATH

Confluentes Mathematici

PELLEGRINI, CLÉMENT¹  NECHITA, ION² 

[1] Département de Mathématique et Statistique, Université d'Ottawa, 585 King Edward, Ottawa, ON, K1N6N5, Canada;Université de Lyon CNRS, Université Lyon 1, Institut Camille Jordan, 43 Bd du 11 Novembre 1918, 69622 Villeurbanne, France

关键词: Quantum trajectory;    stochastic differential equation;    stochastic Schrödinger equation;    open quantum system;   

DOI  :  10.1142/S1793744209000109

学科分类：数学（综合）

来源: World Scientific Publishing Co. Pte. Ltd.

【 摘 要 】

In this paper, 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 [6], where the Gibbs model of heat bath has been studied. It is shown that the statistical model of a heat bath has a 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.

【 授权许可】

Unknown