Quantum chaos on discrete graphs
Mathematical Physics
2007-05-23 v1 math.MP
Abstract
Adapting a method developed for the study of quantum chaos on {\it quantum (metric)} graphs \cite {KS}, spectral 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 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}.
Keywords
Cite
@article{arxiv.0704.3525,
title = {Quantum chaos on discrete graphs},
author = {Uzy Smilansky},
journal= {arXiv preprint arXiv:0704.3525},
year = {2007}
}