Basic properties of nonlinear stochastic Schrödinger equations driven by Brownian motions

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The paper is devoted to the study of nonlinear stochastic Schrödinger equations driven by standard cylindrical Brownian motions (NSSEs) arising from the unraveling of quantum master equations. Under the Born--Markov approximations, this class of stochastic evolutions equations on Hilbert spaces provides characterizations of both continuous quantum measurement processes and the evolution of quantum systems. First, we deal with the existence and uniqueness of regular solutions to NSSEs. Second, we provide two general criteria for the existence of regular invariant measures for NSSEs. We apply our results to a forced and damped quantum oscillator.
Published in at http://dx.doi.org/10.1214/105051607000000311 the Annals of Applied Probability (http://www.imstat.org/aap/) by the Institute of Mathematical Statistics (http://www.imstat.org)

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Probability, 60H15 (Primary) 60H30, 37L40, 81S25, 81P15 (Secondary)

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http://salesiana.dossiersoluciones.com/handle/123456789/212269

Consulte el texto completo en el siguiente enlace:

https://arxiv.org/abs/0804.0121
 http://arxiv.org/abs/0804.0121
 Annals of Applied Probability 2008, Vol. 18, No. 2, 591-619
 doi:10.1214/105051607000000311

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arXiv