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November 2008 Existence, uniqueness and approximation of a stochastic Schrödinger equation: The diffusive case
Clément Pellegrini
Ann. Probab. 36(6): 2332-2353 (November 2008). DOI: 10.1214/08-AOP391

Abstract

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.

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Clément Pellegrini. "Existence, uniqueness and approximation of a stochastic Schrödinger equation: The diffusive case." Ann. Probab. 36 (6) 2332 - 2353, November 2008. https://doi.org/10.1214/08-AOP391

Information

Published: November 2008
First available in Project Euclid: 19 December 2008

zbMATH: 1167.60006
MathSciNet: MR2478685
Digital Object Identifier: 10.1214/08-AOP391

Subjects:
Primary: 60F05, 60G35
Secondary: 60J60

Rights: Copyright © 2008 Institute of Mathematical Statistics

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Vol.36 • No. 6 • November 2008
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