Quantum chaos on discrete graphs

2007/04/26 by Uzy Smilansky, Smilansky, Uzy · 2 citations
Mathematics · Physics and Astronomy · #FOS: Physical sciences #Mathematical Physics (math-ph) #math-ph #math.MP

paper · pdf · doi:10.48550/arxiv.0704.3525

arxiv created 2007/04/26 · arxiv updated 2009/12/01

Abstract

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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