Numerical solution of conservative finite-dimensional stochastic Schrodinger equations

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dc.creatorMora, Carlos M.
dc.date2005-08-25
dc.date.accessioned2026-07-07T05:22:41Z
dc.date.available2026-07-07T05:22:41Z
dc.descriptionThe paper deals with the numerical solution of the nonlinear Ito 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 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.
dc.descriptionPublished at http://dx.doi.org/10.1214/105051605000000403 in the Annals of Applied Probability (http://www.imstat.org/aap/) by the Institute of Mathematical Statistics (http://www.imstat.org)
dc.identifierhttps://arxiv.org/abs/math/0508490
dc.identifierhttp://arxiv.org/abs/math/0508490
dc.identifierAnnals of Applied Probability 2005, Vol. 15, No. 3, 2144-2171
dc.identifierdoi:10.1214/105051605000000403
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/76153
dc.subjectProbability
dc.subject60H35 (Primary) 60H10, 65U05, 65C30 (Secondary)
dc.titleNumerical solution of conservative finite-dimensional stochastic Schrodinger equations
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