Existence, uniqueness and approximation for stochastic Schrodinger equation: the Poisson case
Abstract
In quantum physics, recent investigations deal with the socalled "quantum trajectory" theory. Heuristic rules are usually used to give rise to "stochastic Schrodinger equations" which are stochastic differential equations of nonusual type describing the physical models. These equations pose tedious problems in terms of mathematical justification: notion of solution, existence, uniqueness, justification... In this article, we concentrate on a particular case: the Poisson case. Random measure theory is used in order to give rigorous sense to such equations. We prove existence and uniqueness of a solution for the associated stochastic equation. Furthermore, the stochastic model is physically justified by proving that the solution can be obtained as a limit of a concrete discrete time physical model.
 Publication:

arXiv eprints
 Pub Date:
 September 2007
 arXiv:
 arXiv:0709.3713
 Bibcode:
 2007arXiv0709.3713P
 Keywords:

 Mathematics  Probability;
 Mathematical Physics;
 Quantum Physics
 EPrint:
 35 pages