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Generic quasilocalized and quasiballistic discrete Schrödinger operators


Authors: Silas L. Carvalho and César R. de Oliveira
Journal: Proc. Amer. Math. Soc. 144 (2016), 129-141
MSC (2010): Primary 34L40; Secondary 81Q10, 35J10, 28A80
Published electronically: June 23, 2015
MathSciNet review: 3415583
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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
Email: silas@mat.ufmg.br

César R. de Oliveira
Affiliation: Departamento de Matemática, Universidade Federal de São Carlos, São Carlos, SP, 13560–970 Brazil
Email: oliveira@dm.ufscar.br

DOI: https://doi.org/10.1090/proc/12697
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
Article copyright: © Copyright 2015 American Mathematical Society