Basic properties of nonlinear stochastic Schrodinger equations driven by Brownian motions

• 成果类型: Article
• 署名作者: Mora, Carlos M.; Rebolledo, Rolando
• 署名单位: Universidad de Concepcion; Universidad de Concepcion; Pontificia Universidad Catolica de Chile
• 刊物名称: ANNALS OF APPLIED PROBABILITY
• ISSN/ISSBN: 1050-5164
• DOI: 10.1214/105051607000000311
• 发表日期: 2008
• 页码: 591-619
• 关键词: quantum-state diffusion; differential-equations; semigroups; localization

摘要

The paper is devoted to the study of nonlinear stochastic Schrodinger equations driven by standard cylindrical Brownian motions (NSSEs) arising from the unraveling of quantum master equations. Under the Born-Markov approximations, this class of stochastic evolutions equations on Hilbert spaces provides characterizations of both continuous quantum measurement processes and the evolution of quantum systems. First, we deal with the existence and uniqueness of regular solutions to NSSEs. Second, we provide two general criteria for the existence of regular invariant measures for NSSEs. We apply our results to a forced and damped quantum oscillator.