标题： 耦合单向混沌微波图 显示英文标题

标题： Coupled unidirectional chaotic microwave graphs

摘要： 我们实验研究了由两个耦合的有向部分组成的无向开放微波网络$\Gamma $，这两个有向部分是单向网络$\Gamma_{+} $和$\Gamma_{-} $，对应于其边上运动的两种可能方向。 网络$\Gamma$的二端口散射矩阵被测量，网络的谱统计特性以及弹性增强因子被评估。 将实验共振数与 Weyl 定律预测的理论值进行比较表明，在实验分辨率范围内，共振是双重简并的。 这一结论也通过数值计算得到了证实。 尽管该网络具有时间反演对称性，但缺失的能级谱统计特性以及弹性增强因子与随机矩阵理论中的高斯单位系综预测值非常接近。 我们使用了具有与微波网络$\Gamma$相同结构的开放非耗散量子图的数值计算，来研究谱中的双态结构，否则这些结构在实验中无法分辨。 我们表明，双态尺寸分布接近泊松分布。 显示英文摘要

摘要： We investigate experimentally the undirected open microwave network $\Gamma $ with internal absorption composed of two coupled directed halves, unidirectional networks $\Gamma_{+} $ and $\Gamma_{-} $, corresponding to two possible directions of motion on their edges. The two-port scattering matrix of the network $\Gamma$ 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 $\Gamma$ 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.