Existence, uniqueness and approximation for stochastic Schrodinger equation: the Poisson case

Details Existence, uniqueness and approximation for stochastic Schrodinger equation: the Poisson case Existence, uniqueness and approximation for stochastic Schrodinger equation: the Poisson case

2007-09-24

arxiv.org/abs/0709.3713v2

Mathematics

Probability

35 pages

Scientific paper

In quantum physics, recent investigations deal with the so-called "quantum trajectory" theory. Heuristic rules are usually used to give rise to "stochastic Schrodinger equations" which are stochastic differential equations of non-usual 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.

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