耦合单向混沌微波图
Coupled unidirectional chaotic microwave graphs
AI总结：
本文实验研究由两个单向半部分耦合而成的微波网络，发现其共振呈双重简并，且光谱统计接近高斯幺正系综预测，双重态尺寸分布接近泊松分布。
摘要：
我们实验研究了具有内部吸收的无向开放微波网络 Γ，该网络由两个耦合的有向半部分组成，即单向网络 Γ₊ 和 Γ₋，分别对应其边上两种可能的运动方向。测量了网络 Γ 的双端口散射矩阵，并评估了网络的光谱统计和弹性增强因子。将实验共振数与 Weyl 定律所预言的理论共振数进行比较表明，在实验分辨率范围内，共振是双重简并的。这一结论也得到了数值计算的支持。尽管该网络具有时间反演对称性，但缺失能级光谱统计和弹性增强因子相当接近随机矩阵理论中的高斯幺正系综预测。我们利用与微波网络 Γ 具有相同结构的开放无耗散量子图进行数值计算，以研究光谱中的双重态结构，否则这些结构在实验上无法分辨。我们表明双重态尺寸分布接近泊松分布。
英文摘要：
We investigate experimentally the undirected open microwave network $Γ$ with internal absorption composed of two coupled directed halves, unidirectional networks $Γ_{+} $ and $Γ_{-} $, corresponding to two possible directions of motion on their edges. The two-port scattering matrix of the network $Γ$ is measured and the spectral statistics and the elastic enhancement factor of the network are evaluated. The comparison of the number of experimental resonances with the theoretical one predicted by the Weyl's law shows that within the experimental resolution the resonances are doubly degenerate. This conclusion was also corroborated by the numerical calculations. Though the network is characterized by the time reversal symmetry the missing level spectral statistics and the elastic enhancement factor are rather close to the Gaussian unitary ensemble predictions in random matrix theory. We used numerical calculations for the open non-dissipative quantum graph possessing the same structure as the microwave network $Γ$ to investigate the doublet structures in the spectrum which otherwise would not be experimentally resolved. We show that the doublet size distribution is close to the Poisson distribution.
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