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

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  • Pellegrini, Clément

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.

Suggested Citation

  • Pellegrini, Clément, 2010. "Existence, uniqueness and approximation of the jump-type stochastic Schrodinger equation for two-level systems," Stochastic Processes and their Applications, Elsevier, vol. 120(9), pages 1722-1747, August.
    • Handle: RePEc:eee:spapps:v:120:y:2010:i:9:p:1722-1747
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    References listed on IDEAS

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    1. Belavkin, Viacheslav P., 1992. "Quantum stochastic calculus and quantum nonlinear filtering," Journal of Multivariate Analysis, Elsevier, vol. 42(2), pages 171-201, August.
    2. Barchielli, A. & Holevo, A. S., 1995. "Constructing quantum measurement processes via classical stochastic calculus," Stochastic Processes and their Applications, Elsevier, vol. 58(2), pages 293-317, August.
    3. Sébastien Gleyzes & Stefan Kuhr & Christine Guerlin & Julien Bernu & Samuel Deléglise & Ulrich Busk Hoff & Michel Brune & Jean-Michel Raimond & Serge Haroche, 2007. "Quantum jumps of light recording the birth and death of a photon in a cavity," Nature, Nature, vol. 446(7133), pages 297-300, March.
    4. Nicola Bruti-Liberati & Eckhard Platen, 2005. "On the Strong Approximation of Jump-Diffusion Processes," Research Paper Series 157, Quantitative Finance Research Centre, University of Technology, Sydney.
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    Cited by:

    1. Maryam Siddiqui & Mhamed Eddahbi & Omar Kebiri, 2023. "Numerical Solutions of Stochastic Differential Equations with Jumps and Measurable Drifts," Mathematics, MDPI, vol. 11(17), pages 1-14, August.

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