Relationship between scattering matrix and spectrum of quantum graphs

Details Relationship between scattering matrix and spectrum of quantum graphs Relationship between scattering matrix and spectrum of quantum graphs

2008-01-28

arxiv.org/abs/0801.4104v2

Trans. Amer. Math. Soc. 362 (2010), 6261-6277

Physics

Mathematical Physics

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

Scientific paper

10.1090/S0002-9947-2010-04897-4

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.

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