Communications in Mathematical Physics

, Volume 234, Issue 2, pp 191–227 | Cite as

Spectral Analysis of Unitary Band Matrices

  • Olivier Bourget
  • James S. Howland
  • Alain Joye

Abstract:

 This paper is devoted to the spectral properties of a class of unitary operators with a matrix representation displaying a band structure. Such band matrices appear as monodromy operators in the study of certain quantum dynamical systems. These doubly infinite matrices essentially depend on an infinite sequence of phases which govern their spectral properties. We prove the spectrum is purely singular for random phases and purely absolutely continuous in case they provide the doubly infinite matrix with a periodic structure in the diagonal direction. We also study some properties of the singular spectrum of such matrices considered as infinite in one direction only.

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Copyright information

© Springer-Verlag Berlin Heidelberg 2003

Authors and Affiliations

  • Olivier Bourget
    • 1
  • James S. Howland
    • 2
  • Alain Joye
    • 1
  1. 1.Institut Fourier, Université de Grenoble 1, BP 74, 38402 St.-Martin d'Hères, FranceFR
  2. 2.Department of Mathematics, University of Virginia, Charlottesville, VA 22903, USAUS

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