Generic quasilocalized and quasiballistic discrete Schrödinger operators

Carvalho, Silas; de Oliveira, César

doi:10.1090/proc/12697

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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