时间反演对称性的动力学“破缺”与逆量子遍历性
Dynamical "breaking" of time reversal symmetry and converse quantum ergodicity
摘要：
通常假设具有时间反演不变性和经典混沌动力学的量子系统具有根据GOE型统计分布的能谱。在这里，我们提出了一类系统，不遵循这一规则。我们证明了具有时间反演对称性和“几乎”混沌动力学的等宽凸台球的能级分布是GUE型的。这种效果是由于缺乏遍历性的“动量”的相空间的一部分，正如我们所认为的，是通用的二维。此外，我们表明，某些台球的常宽多连通域的兴趣有关的量子遍历性问题。这些台球是量子遍历，但不是经典遍历。
英文摘要：
It is a common assumption that quantum systems with time reversal invariance and classically chaotic dynamics have energy spectra distributed according to GOE-type of statistics. Here we present a class of systems which fail to follow this rule. We show that for convex billiards of constant width with time reversal symmetry and "almost" chaotic dynamics the energy level distribution is of GUE-type. The effect is due to the lack of ergodicity in the "momentum" part of the phase space and, as we argue, is generic in two dimensions. Besides, we show that certain billiards of constant width in multiply connected domains are of interest in relation to the quantum ergodicity problem. These billiards are quantum ergodic, but not classically ergodic.
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