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Quantum Bernoulli noises approach to Stochastic Schrödinger equation of exclusion type
Journal of Mathematical Physics ( IF 1.3 ) Pub Date : 2020-06-01 , DOI: 10.1063/1.5138370
Suling Ren 1 , Caishi Wang 1 , Yuling Tang 1
Affiliation  

Stochastic Schrodinger equations are a special type of stochastic evolution equations in complex Hilbert spaces, which arise in the study of open quantum systems. Quantum Bernoulli noises refer to annihilation and creation operators acting on Bernoulli functionals, which satisfy a canonical anti-commutation relation in equal time. In this paper, we investigate a linear stochastic Schrodinger equation of exclusion type in terms of quantum Bernoulli noises. Among others, we prove the well-posedness of the equation, illustrate the results with examples, and discuss the consequences. Our main work extends that of Chen and Wang [J. Math. Phys. 58(5), 053510 (2017)].

中文翻译:

排除型随机薛定谔方程的量子伯努利噪声方法

随机薛定谔方程是复杂希尔伯特空间中的一种特殊类型的随机演化方程,它出现在开放量子系统的研究中。量子伯努利噪声是指作用于伯努利泛函的湮灭算子和创造算子,它们在相等的时间内满足规范的反对易关系。在本文中,我们研究了基于量子伯努利噪声的排除型线性随机薛定谔方程。其中,我们证明了方程的适定性,用例子说明了结果,并讨论了结果。我们的主要工作扩展了 Chen 和 Wang [J. 数学。物理。58(5), 053510 (2017)]。
更新日期:2020-06-01
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