Numerical solution of conservative finite-dimensional stochastic Schrodinger equations

• 成果类型: Article
• 署名作者: Mora, CM
• 署名单位: Universidad de Concepcion
• 刊物名称: ANNALS OF APPLIED PROBABILITY
• ISSN/ISSBN: 1050-5164
• DOI: 10.1214/105051605000000403
• 发表日期: 2005
• 页码: 2144-2171
• 关键词: local linearization method; differential-equations; exponential integrators; lyapunov exponents; approximations; CONVERGENCE; simulation

摘要

The paper deals with the numerical solution of the nonlinear lto stochastic differential equations (SDEs) appearing in the unravelling of quantum master equations. We first develop an exponential scheme of weak order I for general globally Lipschitz SDEs governed by Brownian motions. Then, we proceed to study the numerical integration of a class of locally Lipschitz SDEs. More precisely, we adapt the exponential scheme obtained in the first part of the work to the characteristics of certain finite-dimensional nonlinear stochastic Schrodinger equations. This yields a numerical method for the simulation of the mean value of quantum observables. We address the rate of convergence arising in this computation. Finally, an experiment with a representative quantum master equation illustrates the good performance of the new scheme.