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首页> 外文期刊>Letters in Mathematical Physics: A Journal for the Rapid Dissemination of Short Contributions in the Field of Mathematical Physics >A remark on the mean-field dynamics of many-body bosonic systems with random interactions and in a random potential
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A remark on the mean-field dynamics of many-body bosonic systems with random interactions and in a random potential

机译：关于具有随机相互作用和随机势的多体玻色子系统的平均场动力学的评论

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摘要

The mean-field limit for the dynamics of bosons with random two-body interactions and in the presence of a random external potential is rigorously studied, both for the Hartree dynamics and the Gross-Pitaevskii dynamics. First, it is shown that, for interactions and potentials that are almost surely bounded, the many-body quantum evolution can be replaced in the mean-field limit by a single particle nonlinear evolution that is described by the Hartree equation. This is an Egorov-type theorem for many-body quantum systems with random interactions. The analysis is then extended to derive the Gross-Pitaevskii equation with random interactions.
机译：对于Hartree动力学和Gross-Pitaevskii动力学，都严格研究了具有随机两体相互作用且存在外部随机势的玻色子动力学的平均场极限。首先，表明，对于几乎确定有界的相互作用和势能，多体量子演化可以在平均场极限内用由Hartree方程描述的单粒子非线性演化代替。这是具有随机相互作用的多体量子系统的Egorov型定理。然后扩展分析以导出具有随机相互作用的Gross-Pitaevskii方程。

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