Localization for one-dimensional, continuum, Bernoulli-Anderson models

David Damanik, Robert Sims, Günter Stolz

Research output: Contribution to journalArticlepeer-review

49 Scopus citations

Abstract

We use scattering theoretic methods to prove strong dynamical and exponential localization for one-dimensional, continuum, Anderson-type models with singular distributions; in particular, the case of a Bernoulli distribution is covered. The operators we consider model alloys composed of at least two distinct types of randomly dispersed atoms. Our main tools are the reflection and transmission coefficients for compactly supported single-site perturbations of a periodic background which we use to verify the necessary hypotheses of multi-scale analysis. We show that nonreflectionless single sites lead to a discrete set of exceptional energies away from which localization occurs.

Original languageEnglish (US)
Pages (from-to)59-100
Number of pages42
JournalDuke Mathematical Journal
Volume114
Issue number1
DOIs
StatePublished - Jul 15 2002
Externally publishedYes

ASJC Scopus subject areas

  • Mathematics(all)

Fingerprint

Dive into the research topics of 'Localization for one-dimensional, continuum, Bernoulli-Anderson models'. Together they form a unique fingerprint.

Cite this