Open Access
April 2008 Basic properties of nonlinear stochastic Schrödinger equations driven by Brownian motions
Carlos M. Mora, Rolando Rebolledo
Ann. Appl. Probab. 18(2): 591-619 (April 2008). DOI: 10.1214/105051607000000311

Abstract

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.

Citation

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Carlos M. Mora. Rolando Rebolledo. "Basic properties of nonlinear stochastic Schrödinger equations driven by Brownian motions." Ann. Appl. Probab. 18 (2) 591 - 619, April 2008. https://doi.org/10.1214/105051607000000311

Information

Published: April 2008
First available in Project Euclid: 20 March 2008

zbMATH: 1145.60036
MathSciNet: MR2399706
Digital Object Identifier: 10.1214/105051607000000311

Subjects:
Primary: 60H15
Secondary: 37L40 , 60H30 , 81P15 , 81S25

Keywords: existence and uniqueness of solutions , Nonlinear stochastic Schrödinger equations , quantum mechanics , regular invariant measures , stochastic evolution equations

Rights: Copyright © 2008 Institute of Mathematical Statistics

Vol.18 • No. 2 • April 2008
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