Form factor expansion for large graphs: a diagrammatic approach

Details Form factor expansion for large graphs: a diagrammatic approach Form factor expansion for large graphs: a diagrammatic approach

2006-04-11

arxiv.org/abs/nlin/0604025v1

Nonlinear Sciences

Chaotic Dynamics

15 pages, 5 figures, to appear in "Proceedings of Joint Summer Research Conference on Quantum Graphs and Their Applications",

Scientific paper

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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