Abel Klein

A New Proof of Localization in the Anderson Tight Binding Model

We give a new proof of exponential localization in the Anderson tight binding model which uses many ideas of the Frohlich, Martinelli, Scoppola and Spencer proof, but is technically simpler-particularly the probabilistic estimates.

Anderson localization for Bernoulli and other singular potentials

We prove exponential localization in the Anderson model under very weak assumptions on the potential distribution. In one dimension we allow any measure which is not concentrated on a single point and possesses some finite moment. In particular this solves the longstanding problem of localization for Bernoulli potentials (i.e., potentials that take only two values). In dimensions greater than one we prove localization at high disorder for potentials with Hölder continuous distributions and for bounded potentials whose distribution is a convex combination of a Hölder continuous distribution with high disorder and an arbitrary distribution. These include potentials with singular distributions.We also show that for certain Bernoulli potentials in one dimension the integrated density of states has a nontrivial singular component.

LOCALIZATION OF CLASSICAL WAVES. I: ACOUSTIC WAVES

AbstractWe consider classical acoustic waves in a medium described by a position dependent mass density ϱ(x). We assume that ϱ(x) is a reandom perturbation of a periodic function ϱ0(x) and that the periodic acoustic operator

Stochastic processes associated with KMS states

A_0 = - \nabla \cdot \tfrac{1}{{\varrho _0 (x)}}\nabla

New Characterizations of the Region of Complete Localization for Random Schrödinger Operators

has a gap in the spectrum. We prove the existence of localized waves, i.e., finite energy solutions of the acoustic equations with the property that almost all of the waves energy remains in a fixed bounded region of space at all times, with probability one. Localization of acoustic waves is a consequence of Anderson localization for the self-adjoint operators

Generalized Eigenvalue-Counting Estimates for the Anderson Model

A = - \nabla \cdot \tfrac{1}{{\varrho _0 (x)}}\nabla