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Form factor expansion for large graphs: a diagrammatic approach

Gregory Berkolaiko
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Abstract

The form factor of a quantum graph is a function measuring correlations within the spectrum of the graph. It can be expressed as a double sum over the periodic orbits on the graph. We propose a scheme which allows one to evaluate the periodic orbit sum for a special family of graphs and thus to recover the expression for the form factor predicted by the Random Matrix Theory. The scheme, although producing the expected answer, undercounts orbits of a certain structure, raising doubts about an analogous summation recently proposed for quantum billiards.

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Gregory Berkolaiko. 2006-04-11. Form factor expansion for large graphs: a diagrammatic approach. https://arxiv.org/abs/nlin/0604025

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