作为S矩阵极点计数器的复Wigner时延统计：理论与实验
Statistics of Complex Wigner Time Delays as a counter of S-matrix poles: Theory and Experiment
摘要：
研究了亚么正波混沌散射系统的Wigner时延$τ_\text{W}$复推广的统计性质。我们首先从理论上证明了具有均匀吸收强度$η$的系统的$\text{Re}[τ_\text{W}]$分布函数的平均值等于虚部超过$η$的散射矩阵极点的分数。该理论进行了实验测试，无论是一个或两个散射通道的微波图形合奏，并显示打破时间反演不变性和可变的均匀衰减。实验结果与发展的理论非常一致。测量了实部和虚部时延分布的尾部，也发现与理论相符。所得结果适用于短波范围内任意波混沌散射系统的实际实现。
英文摘要：
We study the statistical properties of the complex generalization of Wigner time delay $τ_\text{W}$ for sub-unitary wave chaotic scattering systems. We first demonstrate theoretically that the mean value of the $\text{Re}[τ_\text{W}]$ distribution function for a system with uniform absorption strength $η$ is equal to the fraction of scattering matrix poles with imaginary parts exceeding $η$. The theory is tested experimentally with an ensemble of microwave graphs with either one or two scattering channels, and showing broken time-reversal invariance and variable uniform attenuation. The experimental results are in excellent agreement with the developed theory. The tails of the distributions of both real and imaginary time delay are measured and are also found to agree with theory. The results are applicable to any practical realization of a wave chaotic scattering system in the short-wavelength limit.
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