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Proceedings of the American Mathematical Society

Published by the American Mathematical Society, the Proceedings of the American Mathematical Society (PROC) is devoted to research articles of the highest quality in all areas of pure and applied mathematics.

ISSN 1088-6826 (online) ISSN 0002-9939 (print)

The 2020 MCQ for Proceedings of the American Mathematical Society is 0.85.

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Generic quasilocalized and quasiballistic discrete Schrödinger operators
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by Silas L. Carvalho and César R. de Oliveira PDF
Proc. Amer. Math. Soc. 144 (2016), 129-141 Request permission

Abstract:

We derive sufficient conditions for the presence of generic sets of discrete Schrödinger operators on $l^2(\mathbb Z^d)$, $d\ge 1$, with both quasilocalized and quasiballistic dynamics, and apply them to three operator spaces, that is, with uniformly bounded, analytic quasiperiodic and unbounded potentials. It is concluded, for these spaces, that the dynamics is typically (from the topological viewpoint) nontrivial, whereas quantum intermittency is exceptional.
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Additional Information
  • Silas L. Carvalho
  • Affiliation: Departamento de Matemática, Universidade Federal de Minas Gerais, Belo Horizonte, MG, 30161-970 Brazil
  • MR Author ID: 897765
  • Email: silas@mat.ufmg.br
  • César R. de Oliveira
  • Affiliation: Departamento de Matemática, Universidade Federal de São Carlos, São Carlos, SP, 13560–970 Brazil
  • MR Author ID: 206915
  • Email: oliveira@dm.ufscar.br
  • Received by editor(s): February 16, 2014
  • Received by editor(s) in revised form: November 17, 2014
  • Published electronically: June 23, 2015
  • Communicated by: Michael Hitrik
  • © Copyright 2015 American Mathematical Society
  • Journal: Proc. Amer. Math. Soc. 144 (2016), 129-141
  • MSC (2010): Primary 34L40; Secondary 81Q10, 35J10, 28A80
  • DOI: https://doi.org/10.1090/proc/12697
  • MathSciNet review: 3415583