Existence, uniqueness and approximation for stochastic Schrodinger equation: the Poisson caseReport as inadecuate




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1 ICJ - Institut Camille Jordan Villeurbanne

Abstract : 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.

Keywords : stochastic differential equation random measure Euler scheme Poisson approximation coupling method quantum trajectory





Author: Clement Pellegrini -

Source: https://hal.archives-ouvertes.fr/



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