Relationship between scattering matrix and spectrum of quantum graphs

Abstract

We investigate the equivalence between spectral characteristics of the Laplace operator on a metric graph, and the associated unitary scattering operator. We prove that the statistics of level spacings, and moments of observations in the eigenbases coincide in the limit that all bond lengths approach a positive constant value.

19 pages, 3 figures; substituted a proof for a reference to a published one, other minor updates

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