Existence, uniqueness and approximation of a stochastic Schrödinger equation: the diffusive case

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dc.creatorPellegrini, Clément
dc.date2007-09-11
dc.date2009-01-21
dc.date.accessioned2026-07-07T12:58:43Z
dc.date.available2026-07-07T12:58:43Z
dc.descriptionRecent developments in quantum physics make heavy use of so-called "quantum trajectories." Mathematically, this theory gives rise to "stochastic Schrödinger equations", that is, perturbation of Schrödinger-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 Schrödinger 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.
dc.descriptionPublished in at http://dx.doi.org/10.1214/08-AOP391 the Annals of Probability (http://www.imstat.org/aop/) by the Institute of Mathematical Statistics (http://www.imstat.org)
dc.identifierhttps://arxiv.org/abs/0709.1703
dc.identifierhttp://arxiv.org/abs/0709.1703
dc.identifierAnnals of Probability 2008, Vol. 36, No. 6, 2332-2353
dc.identifierdoi:10.1214/08-AOP391
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/225339
dc.subjectProbability
dc.subjectMathematical Physics
dc.subjectQuantum Physics
dc.subject60F05, 60G35 (Primary), 60J60 (Secondary)
dc.titleExistence, uniqueness and approximation of a stochastic Schrödinger equation: the diffusive case
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