Existence, uniqueness and approximation of a stochastic Schrödinger equation: The diffusive case
Pellegrini, Clément
Ann. Probab., Tome 36 (2008) no. 1, p. 2332-2353 / Harvested from Project Euclid
Recent developments in quantum physics make heavy use of so-called “quantum trajectories.” Mathematically, this theory gives rise to “stochastic Schrödinger equations,” that is, perturbation of Schrödinger-type equations under the form of stochastic differential equations. But such equations are in general not of the usual type as considered in the literature. They pose a serious problem in terms of justifying the existence and uniqueness of a solution, justifying the physical pertinence of the equations. In this article we concentrate on a particular case: the diffusive case, for a two-level system. We prove existence and uniqueness of the associated stochastic Schrödinger equation. We physically justify the equations by proving that they are a continuous-time limit of a concrete physical procedure for obtaining a quantum trajectory.
Publié le : 2008-11-15
Classification:  Quantum trajectory,  stochastic integral convergence,  stochastic process,  60F05,  60G35,  60J60
@article{1229696605,
     author = {Pellegrini, Cl\'ement},
     title = {Existence, uniqueness and approximation of a stochastic Schr\"odinger equation: The diffusive case},
     journal = {Ann. Probab.},
     volume = {36},
     number = {1},
     year = {2008},
     pages = { 2332-2353},
     language = {en},
     url = {http://dml.mathdoc.fr/item/1229696605}
}
Pellegrini, Clément. Existence, uniqueness and approximation of a stochastic Schrödinger equation: The diffusive case. Ann. Probab., Tome 36 (2008) no. 1, pp.  2332-2353. http://gdmltest.u-ga.fr/item/1229696605/