Lu Junjie, Che Jiongning, Zhang Xiaodong, Dietz Barbara
School of Physical Science and Technology, and Key Laboratory for Magnetism and Magnetic Materials of MOE, Lanzhou University, Lanzhou, Gansu 730000, China.
Phys Rev E. 2020 Aug;102(2-1):022309. doi: 10.1103/PhysRevE.102.022309.
We present experimental and numerical results for the parametric fluctuation properties in the spectra of classically chaotic quantum graphs with unitary or symplectic symmetry. A level dynamics is realized by changing the lengths of a few bonds parametrically. The long-range correlations in the spectra reveal at a fixed parameter value deviations from those expected for generic chaotic systems with corresponding universality class. They originate from modes which are confined to individual bonds or explore only a fraction of the quantum graph. Similarly, discrepancies are observed in the avoided-crossing distribution, velocity correlation function, and the curvature distribution of the level dynamics which also may be attributed to such localized modes. We demonstrate that these may be easily identified by inspecting the level dynamics and consequently their nonuniversal contributions to the parametric spectral properties may be diminished considerably. This is corroborated by numerical studies.
我们给出了具有酉对称性或辛对称性的经典混沌量子图谱中参数涨落特性的实验和数值结果。通过参数化改变少数键的长度来实现能级动力学。谱中的长程相关性在固定参数值下揭示了与具有相应普适类的一般混沌系统预期情况的偏差。它们源于局限于单个键或仅探索量子图一部分的模式。类似地，在能级动力学的避免交叉分布、速度相关函数和曲率分布中也观察到差异，这些差异也可能归因于此类局域模式。我们证明，通过检查能级动力学可以很容易地识别这些模式，因此它们对参数谱特性的非普适贡献可以大大减少。数值研究证实了这一点。
