Browsing by Author "Mora, Carlos M."

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    Basic properties of nonlinear stochastic Schrodinger equations driven by Brownian motions
    (INST MATHEMATICAL STATISTICS, 2008) Mora, Carlos M.; Rebolledo, Rolando
    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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    Regularity of solutions to linear stochastic Schrodinger equations
    (WORLD SCIENTIFIC PUBL CO PTE LTD, 2007) Mora, Carlos M.; Rebolledo, Rolando
    We develop linear stochastic Schrodinger equations driven by standard cylindrical Brownian motions (LSSs) that unravel quantum master equations in Lindblad form into quantum trajectories. More precisely, this paper establishes the existence and uniqueness of the smooth strong solution X-t to a LSS with regular initial condition. Moreover, we obtain that the mean value of the square norm of X-t is constant. We also treat the approximation of LSSs by ordinary stochastic differential equations. We apply our results to: