The Annals of Applied Probability

Numerical solution of conservative finite-dimensional stochastic Schrödinger equations

Carlos M. Mora

Full-text: Open access

Abstract

The paper deals with the numerical solution of the nonlinear Itô stochastic differential equations (SDEs) appearing in the unravelling of quantum master equations. We first develop an exponential scheme of weak order 1 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 Schrödinger 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.

Article information

Source
Ann. Appl. Probab., Volume 15, Number 3 (2005), 2144-2171.

Dates
First available in Project Euclid: 15 July 2005

Permanent link to this document
https://projecteuclid.org/euclid.aoap/1121433780

Digital Object Identifier
doi:10.1214/105051605000000403

Mathematical Reviews number (MathSciNet)
MR2152256

Zentralblatt MATH identifier
1083.60058

Subjects
Primary: 60H35: Computational methods for stochastic equations [See also 65C30]
Secondary: 60H10: Stochastic ordinary differential equations [See also 34F05] 65U05 65C30: Stochastic differential and integral equations

Keywords
Stochastic Schrödinger equation stochastic differential equations quantum master equations numerical solution exponential schemes rate of convergence weak convergence

Citation

Mora, Carlos M. Numerical solution of conservative finite-dimensional stochastic Schrödinger equations. Ann. Appl. Probab. 15 (2005), no. 3, 2144--2171. doi:10.1214/105051605000000403. https://projecteuclid.org/euclid.aoap/1121433780


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