标题： 时间反演对称性的动态“破坏”与逆向量子遍历性 显示英文标题

标题： Dynamical "breaking" of time reversal symmetry and converse quantum ergodicity

摘要： 这是一个常见的假设，即具有时间反演对称性和经典混沌动力学的量子系统，其能量谱按照GOE类型的统计分布。 在这里，我们提出了一类不符合这一规则的系统。 我们证明，对于具有时间反演对称性和“几乎”混沌动力学的等宽凸散射器，能级分布为GUE类型。 这种效应是由于相空间中“动量”部分缺乏遍历性，我们认为在二维情况下这是普遍的。 此外，我们表明，在多连通区域中的某些等宽散射器在与量子遍历性问题相关时具有研究价值。 这些散射器是量子遍历的，但不是经典遍历的。 显示英文摘要

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.