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

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

doi:10.1142/s0129055x15500075

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

Professor Norbert Peyerimhoff norbert.peyerimhoff@durham.ac.uk
Professor

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.

Citation

Leonhardt, K., Peyerimhoff, N., Tautenhahn, M., & Veselic, I. (2015). Wegner estimate and localization for alloy-type models with sign-changing exponentially decaying single-site potentials. Reviews in Mathematical Physics, 27(04), https://doi.org/10.1142/s0129055x15500075

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
Related Public URLs	http://arxiv.org/pdf/1309.0109v2.pdf