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Transactions of the American Mathematical Society

Published by the American Mathematical Society since 1900, Transactions of the American Mathematical Society is devoted to longer research articles in all areas of pure and applied mathematics.

ISSN 1088-6850 (online) ISSN 0002-9947 (print)

The 2020 MCQ for Transactions of the American Mathematical Society is 1.48.

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Relationship between scattering matrix and spectrum of quantum graphs
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by G. Berkolaiko and B. Winn PDF
Trans. Amer. Math. Soc. 362 (2010), 6261-6277 Request permission

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.
References
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Additional Information
  • G. Berkolaiko
  • Affiliation: Department of Mathematics, Texas A&M University, College Station, Texas 77843-3368
  • MR Author ID: 366171
  • 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
  • Received by editor(s): March 21, 2008
  • Published electronically: July 14, 2010
  • © Copyright 2010 American Mathematical Society
    The copyright for this article reverts to public domain 28 years after publication.
  • 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
  • MathSciNet review: 2678973