共振的随机矩阵理论综述
Random Matrix Theory of Resonances: an Overview
摘要：
电磁波在台球状系统中的散射已经成为研究量子混沌特性的标准实验工具。随机矩阵理论（RMT）描述了本征频率和相关本征函数的统计仍然是量子混沌系统理论理解的支柱之一。在散射系统中，通过天线耦合到连续体将实本征频率转换为复频率平面中的散射矩阵的极点，并将相关本征函数转换为衰减的共振态。了解这些极点的统计数据，以及RMT方法中相关的非正交共振本征函数仍然是可能的，尽管更具挑战性的任务。
英文摘要：
Scattering of electromagnetic waves in billiard-like systems has become a standard experimental tool of studying properties associated with Quantum Chaos. Random Matrix Theory (RMT) describing statistics of eigenfrequencies and associated eigenfunctions remains one of the pillars of theoretical understanding of quantum chaotic systems. In a scattering system coupling to continuum via antennae converts real eigenfrequencies into poles of the scattering matrix in the complex frequency plane and the associated eigenfunctions into decaying resonance states. Understanding statistics of these poles, as well as associated non-orthogonal resonance eigenfunctions within RMT approach is still possible, though much more challenging task.
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