具有辛对称性的微波图的谱和谱相关
Spectra and spectral correlations of microwave graphs with symplectic symmetry
摘要：
根据Joyner等人的想法[EPL，107（2014）50004]，已经实现了具有服从T^2=-1的反对酉对称性T的微波图。这种系统所预期的Kramers双峰已经被清楚地识别出来，并且可以通过破坏反幺正对称性的微扰来解除。所观察到的Kramers双峰的光谱级间距分布与高斯辛系综（GSE）的预测一致，预期混沌系统具有这样的对称性。此外，还给出了两点关联函数、谱形状因子、数方差和谱刚度的结果，以及通过连续改变T从T^2=-1到T^2=1从GSE到GOE统计的过渡的结果。
英文摘要：
Following an idea by Joyner et al. [EPL, 107 (2014) 50004] a microwave graph with antiunitary symmetry T obeying T^2=-1 has been realized. The Kramers doublets expected for such systems have been clearly identified and could be lifted by a perturbation which breaks the antiunitary symmetry. The observed spectral level spacings distribution of the Kramers doublets is in agreement with the predictions from the Gaussian symplectic ensemble (GSE), expected for chaotic systems with such a symmetry. In addition results on the two-point correlation function, the spectral form factor, the number variance and the spectral rigidity are presented, as well as on the transition from GSE to GOE statistics by continuously changing T from T^2=-1 to T^2=1.
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