标题： 近似单向量子图的谱统计 显示英文标题

标题： Spectral statistics of nearly unidirectional quantum graphs

摘要： 具有时间反演对称性和单向经典动力学的量子图的能量等级是双重简并的，并遵循高斯酉系综的谱统计特性。 然而，当通过奇异扰动在图的一个顶点上破坏单向性时，这些简并性会被消除。 基于随机矩阵模型，我们推导出了此类系统能量等级之间最近邻分布的解析表达式。 正如我们所展示的，结果与具有本征函数均匀分布的图的实际统计结果非常吻合。 然而，对于表现出强疤痕效应的图类，它却显示出相当大的偏差。 显示英文摘要

摘要： The energy levels of a quantum graph with time reversal symmetry and unidirectional classical dynamics are doubly degenerate and obey the spectral statistics of the Gaussian Unitary Ensemble. These degeneracies, however, are lifted when the unidirectionality is broken in one of the graph's vertices by a singular perturbation. Based on a Random Matrix model we derive an analytic expression for the nearest neighbour distribution between energy levels of such systems. As we demonstrate the result agrees excellently with the actual statistics for graphs with a uniform distribution of eigenfunctions. Yet, it exhibits quite substantial deviations for classes of graphs which show strong scarring.