Poisson情形下随机Schrodinger方程解的存在唯一性与逼近
Existence, uniqueness and approximation for stochastic Schrodinger equation: the Poisson case
摘要：
在量子物理学中，最近的研究涉及所谓的“量子轨道”理论。启发式规则通常用于产生“随机薛定谔方程”，其是描述物理模型的非通常类型的随机微分方程。这些方程提出繁琐的问题，在数学理由：概念的解决方案，存在性，唯一性，理由.在这篇文章中，我们集中在一个特殊的情况下：泊松情况。随机测度论被用来给这些方程以严格的意义。我们证明了相关的随机方程的解的存在性和唯一性。此外，通过证明解可以作为具体离散时间物理模型的极限来获得，证明了随机模型的物理合理性。
英文摘要：
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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