拉格朗日状态如何演化成随机波
How Lagrangian states evolve into random waves
摘要：
本文考虑了负曲率紧致流形$(X,d)$和$X$上的一族半经典拉格朗日态$f_h(x) = a(x) e^{\frac{i}{h} ϕ(x)}$.对于一个广泛的家庭的相位$ϕ$，我们表明，$f_h$，当演变的半经典薛定谔方程在很长一段时间内，类似于一个随机高斯场。这可以看作是一个类似的贝里的随机波猜想拉格朗日状态。
英文摘要：
In this paper, we consider a compact manifold $(X,d)$ of negative curvature, and a family of semiclassical Lagrangian states $f_h(x) = a(x) e^{\frac{i}{h} ϕ(x)}$ on $X$. For a wide family of phases $ϕ$, we show that $f_h$, when evolved by the semiclassical Schrödinger equation during a long time, resembles a random Gaussian field. This can be seen as an analogue of Berry's random waves conjecture for Lagrangian states.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
