Anderson Localization Induced by Random Defects of a Ragged Boundary

V. Chulaevsky

2023, v.29, Issue 1, 35-65

ABSTRACT

We study alloy-type Anderson Hamiltonians in finite-width layers in Euclidean spaces and in periodic lattices
of arbitrary dimension. The disorder is induced by random microscopic defects
of the boundary carrying extra potentials of infinite range featuring a power-law decay.
We consider two extreme cases of disorder: with most singular, Bernoulli probability distributions, and
with very regular ones, admitting a bounded probability density. Exponential spectral and sub-exponential dynamical localization
are proved in both cases, by extending the methods of our papers \cite{C18g,C21a} from IID to correlated (Markov)
random fields generating the disorder. In the smooth disorder case, we prove an asymptotically exponential
strong dynamical localization under the optimal condition on the decay rate of the local potentials (summability).

Keywords: Anderson localization; random boundary; Bernoulli disorder

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