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Relationship between scattering matrix and spectrum of quantum graphs


Authors: G. Berkolaiko and B. Winn
Journal: Trans. Amer. Math. Soc. 362 (2010), 6261-6277
MSC (2000): Primary 34L20, 81Q10, 81Q50
DOI: https://doi.org/10.1090/S0002-9947-2010-04897-4
Published electronically: July 14, 2010
MathSciNet review: 2678973
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Abstract | References | Similar Articles | Additional Information

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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Additional Information

G. Berkolaiko
Affiliation: Department of Mathematics, Texas A&M University, College Station, Texas 77843-3368
Email: gregory.berkolaiko@math.tamu.edu

B. Winn
Affiliation: Department of Mathematics, Texas A&M University, College Station, Texas 77843-3368
Address at time of publication: School of Mathematics, Loughborough University, Loughborough, LE11 3TU, United Kingdom

DOI: https://doi.org/10.1090/S0002-9947-2010-04897-4
Received by editor(s): March 21, 2008
Published electronically: July 14, 2010
Article copyright: © Copyright 2010 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.

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