Relationship between scattering matrix and spectrum of quantum graphs

Berkolaiko, G.; Winn, B.

doi:10.1090/S0002-9947-2010-04897-4

Relationship between scattering matrix and spectrum of quantum graphs
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by G. Berkolaiko and B. Winn

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

DOI: https://doi.org/10.1090/S0002-9947-2010-04897-4

Published electronically: July 14, 2010

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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.

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