离散图上的量子混沌
Quantum chaos on discrete graphs
摘要：
采用研究{ \it量子（度量）}图\cite {KS}上量子混沌的方法，导出了图上{ \it离散}拉普拉斯算子的谱$ζ$函数和迹公式.这是通过表示的谱长期方程的周期轨道的图形，并获得属于最初由Ihara \cite {Ihara}提出的$ζ$函数类，并扩大了随后的作者\cite {斯塔克，Sunada}的功能。最后，提出了离散图上的“经典动力学”模型。它类似于量子图\cite {KS}的相应经典动力学。
英文摘要：
Adapting a method developed for the study of quantum chaos on {\it quantum (metric)} graphs \cite {KS}, spectral $ζ$ functions and trace formulae for {\it discrete} Laplacians on graphs are derived. This is achieved by expressing the spectral secular equation in terms of the periodic orbits of the graph, and obtaining functions which belongs to the class of $ζ$ functions proposed originally by Ihara \cite {Ihara}, and expanded by subsequent authors \cite {Stark,Sunada}. Finally, a model of "classical dynamics" on the discrete graph is proposed. It is analogous to the corresponding classical dynamics derived for quantum graphs \cite {KS}.
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