EXISTENCE, UNIQUENESS AND APPROXIMATION OF A STOCHASTIC SCHRODINGER EQUATION: THE DIFFUSIVE CASE

• 成果类型: Article
• 署名作者: Pellegrini, Clement
• 署名单位: Centre National de la Recherche Scientifique (CNRS); Ecole Centrale de Lyon; Institut National des Sciences Appliquees de Lyon - INSA Lyon; Universite Claude Bernard Lyon 1; Universite Jean Monnet
• 刊物名称: ANNALS OF PROBABILITY
• ISSN/ISSBN: 0091-1798
• DOI: 10.1214/08-AOP391
• 发表日期: 2008
• 页码: 2332-2353
• 关键词: limit

摘要

Recent developments in quantum physics make heavy use of so-called quantum trajectories. Mathematically, this theory gives rise to stochastic Schrodinger equations, that is, perturbation of Schrodinger-type equations under the form of stochastic differential equations. But Such equations are in general not of the usual type as considered in the literature. They pose a serious problem in terms of justifying the existence and uniqueness of a Solution, Justifying the physical pertinence of the equations. In this article we concentrate on a particular case: the diffusive case, for a two-level system. We prove existence and uniqueness, of the associated stochastic Schrodinger equation. We physically justify the equations by proving that they are a continuous-time limit of a concrete physical procedure for obtaining a quantum trajectory.