Existence, uniqueness and approximation of the jump-type stochastic Schrodinger equation for two-level systems

STOCHASTIC PROCESSES AND THEIR APPLICATIONS

卷:120

Article

Pellegrini, Clement

关键词: Stochastic Schrodinger equations;    Quantum trajectories;    stochastic differential equation with jump;    Poisson random measure;    Stochastic intensity;    Euler scheme;   

DOI  :  10.1016/j.spa.2010.03.010

来源: Elsevier

【 摘 要 】

In quantum physics, recent investigations deal with the so-called stochastic Schrodinger equations theory. This concerns stochastic differential equations of non-usual-type describing random evolutions of open quantum systems. These equations are often justified with heuristic rules and pose tedious problems in terms of mathematical and physical justifications: notion of solution, existence, uniqueness, etc. In this article, we concentrate on a particular case: the Poisson case. Random Measure theory is used in order to give rigorous sense to such equations. We prove the existence and uniqueness of a solution for the associated stochastic equation. Furthermore, the stochastic model is physically justified by proving that the solution can be obtained as a limit of a concrete discrete time physical model. (C) 2010 Elsevier B.V. All rights reserved.

【 授权许可】

Free