Karsten Leonhardt, Norbert Peyerimhoff, Martin Tautenhahn, Ivan Veselić: Wegner estimate and localization for alloy-type models with sign-changing exponentially decaying single-site potentials

Author(s):

Karsten Leonhardt
Norbert Peyerimhoff
Martin Tautenhahn
Ivan Veselić

Title:

Karsten Leonhardt, Norbert Peyerimhoff, Martin Tautenhahn, Ivan Veselić: Wegner estimate and localization for alloy-type models with sign-changing exponentially decaying single-site potentials

Electronic source:

application/pdf

Preprint series:

Technische Universität Chemnitz, Fakultät für Mathematik (Germany). Preprint 15, 2013

Mathematics Subject Classification:

82B44	[]
60H25	[]
35J10	[]

Abstract:

We study Schrödinger operators on L²(ℝ^d) and l²(ℤ^d) with a random potential of alloy-type. The single-site potential is assumed to be exponentially decaying but not of compact support. 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.

Keywords:

random Schrödinger operators, alloy-type model, discrete alloy-type model, integrated density of states, Wegner estimate, single-site potential

Language:

English

Publication time:

08/2013