论文标题
拉格朗日状态如何演变为随机波
How Lagrangian states evolve into random waves
论文作者
论文摘要
在本文中，我们考虑了负曲率的紧凑型歧管$（x，d）$，以及一个半经典的拉格朗日状态$ f_h（x）= a（x）e^{\ frac {i} {i} {h} {h} ϕ（x）$ x $。对于一个广泛的阶段$ ϕ $的家庭，我们表明$ f_h $在长期以来由半经典的schrödinger方程进化时，类似于随机的高斯领域。这可以看作是贝里对拉格朗日国家的随机波的类似物。
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.
