Existence, uniqueness and approximation of the jump-type stochastic Schrodinger equation for two-level systems

Clément Pellegrini

Stochastic Processes and their Applications, 2010, vol. 120, issue 9, 1722-1747

Abstract: In quantum physics, recent investigations deal with the so-called "stochastic Schrodinger equations" theory. This concerns stochastic differential equations of non-usual-type describing random evolutions of open quantum systems. These equations are often justified with heuristic rules and pose tedious problems in terms of mathematical and physical justifications: notion of solution, existence, uniqueness, etc. 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 the 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; Schrodinger; equations; Quantum; trajectories; stochastic; differential; equation; with; jump; Poisson; random; measure; Stochastic; intensity; Euler; scheme (search for similar items in EconPapers)
Date: 2010
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Citations: View citations in EconPapers (1)

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