时间相关的量子微扰在半经典状态下是均匀的

IF 1.2 2区数学 Q1 MATHEMATICS Indiana University Mathematics Journal Pub Date : 2021-02-09 DOI:10.1512/iumj.2023.72.9363

F. Golse, T. Paul

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引用次数: 0

摘要

我们给出了一个随时间变化的量子扰动结果，对于梯度有界的势，其普朗克常数是均匀的。我们还表明，扰动量子动力学的经典极限仍然在经典未扰动量子动力学的管状邻域中，该邻域的大小为扰动大小的平方根数量级。我们处理薛定谔方程和冯·诺伊曼-海森堡方程。

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Time dependent quantum perturbations uniform in the semiclassical regime

We present a time dependent quantum perturbation result, uniform in the Planck constant for potential whose gradient is bounded a.e..We show also that the classical limit of the perturbed quantum dynamics remains in a tubular neighborhood of the classical unperturbed one, the size of this neighborhood being of the order of the square root of the size of the perturbation. We treat both Schr\"odinger and von Neumann-Heisenberg equations.

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