Basic properties of nonlinear stochastic Schrodinger equations driven by Brownian motions
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Date
2008
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INST MATHEMATICAL STATISTICS
Abstract
The paper is devoted to the study of nonlinear stochastic Schrodinger 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.
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Keywords
nonlinear stochastic Schrodinger equations, regular invariant measures, existence and uniqueness of solutions, quantum mechanics, stochastic evolution equations, QUANTUM-STATE DIFFUSION, DIFFERENTIAL-EQUATIONS, SEMIGROUPS, LOCALIZATION