Che Jiongning, Zhang Xiaodong, Zhang Weihua, Dietz Barbara, Chai Guozhi
Lanzhou Center for Theoretical Physics and the Gansu Provincial Key Laboratory of Theoretical Physics, Lanzhou University, Lanzhou, Gansu 730000, China.
Center for Theoretical Physics of Complex Systems, Institute for Basic Science (IBS), Daejeon 34126, Korea.
Phys Rev E. 2022 Jul;106(1-1):014211. doi: 10.1103/PhysRevE.106.014211.
We present experimental and numerical results for the fluctuation properties in the eigenfrequency spectra and of the scattering matrix of closed and open unidirectional quantum graphs, respectively. Unidirectional quantum graphs, that are composed of bonds connected by reflectionless vertices, were introduced by Akila and Gutkin [Akila and Gutkin, J. Phys. A: Math. Theor. 48, 345101 (2015)1751-811310.1088/1751-8113/48/34/345101]. The nearest-neighbor spacing distribution of their eigenvalues was shown to comply with random-matrix theory predictions for typical chaotic systems with completely violated time-reversal invariance. The occurrence of short periodic orbits confined to a fraction of the system, that lead in conventional quantum graphs to deviations of the long-range spectral correlations from the behavior expected for typical chaotic systems, is suppressed in unidirectional ones. Therefore, we pose the question whether such graphs may serve as a more appropriate model for closed and open chaotic systems with violated time-reversal invariance than conventional ones. We compare the fluctuation properties of their eigenvalues and scattering matrix elements and observe especially in the long-range correlations larger deviations from random-matrix theory predictions for the unidirectional graphs. These are attributed to a loss of complexity of the underlying dynamic, induced by the unidirectionality.
我们分别给出了封闭和开放单向量子图本征频率谱以及散射矩阵涨落特性的实验和数值结果。单向量子图由通过无反射顶点相连的键组成，由阿基拉和古特金引入[阿基拉和古特金，《物理学报A：数学理论》48, 345101 (2015)1751 - 811310.1088/1751 - 8113/48/34/345101]。其本征值的最近邻间距分布被证明符合具有完全破坏时间反演不变性的典型混沌系统的随机矩阵理论预测。在传统量子图中，局限于系统一部分的短周期轨道的出现会导致长程谱相关性偏离典型混沌系统预期的行为，而在单向量子图中这种情况受到抑制。因此，我们提出一个问题，即对于具有破坏时间反演不变性的封闭和开放混沌系统，这种量子图是否可能比传统量子图更适合作为模型。我们比较了它们本征值和散射矩阵元素的涨落特性，特别观察到在长程相关性方面，单向量子图与随机矩阵理论预测的偏差更大。这些偏差归因于由单向性引起的底层动力学复杂性的丧失。
