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.
Publié le : 2008-04-15
Classification:
Nonlinear stochastic Schrödinger equations,
regular invariant measures,
existence and uniqueness of solutions,
quantum mechanics,
stochastic evolution equations,
60H15,
60H30,
37L40,
81S25,
81P15
@article{1206018198,
author = {Mora, Carlos M. and Rebolledo, Rolando},
title = {Basic properties of nonlinear stochastic Schr\"odinger equations driven by Brownian motions},
journal = {Ann. Appl. Probab.},
volume = {18},
number = {1},
year = {2008},
pages = { 591-619},
language = {en},
url = {http://dml.mathdoc.fr/item/1206018198}
}
Mora, Carlos M.; Rebolledo, Rolando. Basic properties of nonlinear stochastic Schrödinger equations driven by Brownian motions. Ann. Appl. Probab., Tome 18 (2008) no. 1, pp. 591-619. http://gdmltest.u-ga.fr/item/1206018198/