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Wegner estimate and localization for alloy-type models with sign-changing exponentially decaying single-site potentials

Leonhardt, Karsten; Peyerimhoff, Norbert; Tautenhahn, Manfred; Veselic, Ivan

Authors

Karsten Leonhardt

Manfred Tautenhahn

Ivan Veselic



Abstract

We study Schrödinger operators on L2(ℝd) and ℓ2(ℤd) with a random potential of alloy-type. The single-site potential is assumed to be exponentially decaying but not necessarily of fixed sign. In the continuum setting, we require a generalized step-function shape. Wegner estimates are bounds on the average number of eigenvalues in an energy interval of finite box restrictions of these types of operators. In the described situation, a Wegner estimate, which is polynomial in the volume of the box and linear in the size of the energy interval, holds. We apply the established Wegner estimate as an ingredient for a localization proof via multiscale analysis.

Journal Article Type Article
Acceptance Date Apr 3, 2015
Online Publication Date May 11, 2015
Publication Date May 11, 2015
Deposit Date Jan 6, 2016
Publicly Available Date Apr 14, 2016
Journal Reviews in Mathematical Physics
Print ISSN 0129-055X
Electronic ISSN 1793-6659
Publisher World Scientific Publishing
Peer Reviewed Peer Reviewed
Volume 27
Issue 04
DOI https://doi.org/10.1142/s0129055x15500075
Public URL https://durham-repository.worktribe.com/output/1392698
Related Public URLs http://arxiv.org/pdf/1309.0109v2.pdf

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