Degeneracies in the length spectra of metric graphs
Mathematical Physics
2009-11-13 v1 math.MP
Abstract
The spectral theory of quantum graphs is related via an exact trace formula with the spectrum of the lengths of periodic orbits (cycles) on the graphs. The latter is a degenerate spectrum, and understanding its structure (i.e.,finding out how many different lengths exist for periodic orbits with a given period and the average number of periodic orbits with the same length) is necessary for the systematic study of spectral fluctuations using the trace formula. This is a combinatorial problem which we solve exactly for complete (fully connected) graphs with arbitrary number of vertices.
Keywords
Cite
@article{arxiv.0807.2903,
title = {Degeneracies in the length spectra of metric graphs},
author = {U. Gavish and U. Smilansky},
journal= {arXiv preprint arXiv:0807.2903},
year = {2009}
}
Comments
13 pages, 7 figures