Leonhardt, Karsten and Peyerimhoff, Norbert and Tautenhahn, Manfred and Veselic, Ivan (2015) 'Wegner estimate and localization for alloy-type models with sign-changing exponentially decaying single-site potentials.', Reviews in mathematical physics., 27 (04). p. 1550007.
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.
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|Publisher Web site:||http://dx.doi.org/10.1142/S0129055X15500075|
|Publisher statement:||Electronic version of an article published as Reviews in mathematical physics, 27, 4, 2015, 1550007, 10.1142/S0129055X15500075 © 2015 World Scientific Publishing Co. http://www.worldscientific.com/worldscinet/rmp|
|Date accepted:||03 April 2015|
|Date deposited:||No date available|
|Date of first online publication:||11 May 2015|
|Date first made open access:||No date available|
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