State Key Laboratory for Mesoscopic Physics and School of Physics, Peking University; Collaborative Innovation Center of Quantum Matter, Beijing 100871, China.
Institute for Advanced Study, Tsinghua University, Beijing 100084, China.
Phys Rev E. 2016 Apr;93(4):040201. doi: 10.1103/PhysRevE.93.040201. Epub 2016 Apr 4.
Distributions of eigenmodes are widely concerned in both bounded and open systems. In the realm of chaos, counting resonances can characterize the underlying dynamics (regular vs chaotic), and is often instrumental to identify classical-to-quantum correspondence. Here, we study, both theoretically and experimentally, the statistics of chaotic resonances in an optical microcavity with a mixed phase space of both regular and chaotic dynamics. Information on the number of chaotic modes is extracted by counting regular modes, which couple to the former via dynamical tunneling. The experimental data are in agreement with a known semiclassical prediction for the dependence of the number of chaotic resonances on the number of open channels, while they deviate significantly from a purely random-matrix-theory-based treatment, in general. We ascribe this result to the ballistic decay of the rays, which occurs within Ehrenfest time, and importantly, within the time scale of transient chaos. The present approach may provide a general tool for the statistical analysis of chaotic resonances in open systems.
本征模的分布在有界和开放系统中都受到广泛关注。在混沌领域，共振计数可以表征潜在的动力学（规则与混沌），并且通常有助于确定经典到量子的对应关系。在这里，我们从理论和实验两方面研究了具有正则和混沌动力学混合相空间的光学微腔中混沌共振的统计特性。通过计数与前者通过动力学隧道耦合的正则模式，可以提取有关混沌模式数量的信息。实验数据与已知的半经典预测一致，表明混沌共振的数量与开放通道的数量有关，而与纯粹基于随机矩阵理论的处理方法有很大差异。我们将这一结果归因于射线的弹道衰减，它发生在 Ehrenfest 时间内，并且重要的是，在瞬态混沌的时间尺度内。这种方法可能为开放系统中混沌共振的统计分析提供一种通用工具。
