Lifshitz tails and localization in the three-dimensional anderson model

Alexander Elgart

Research output: Contribution to journalArticlepeer-review

10 Scopus citations

Abstract

Consider the three-dimensional Anderson model with a zero mean and bounded independent, identically distributed random potential. Let λ be the coupling constant measuring the strength of the disorder, and let σ(E) be the self-energy of the model at energy E. For any ε >0 and sufficiently small λ, we derive almost-sure localization in the bandE ≤ -σ(0)-λ4-ε. In this energy region, we show that the typical correlation length ξE behaves roughly asO ((|E|-σ(E))-1/2), completing the argument outlined in the preprint of T. Spencer [18].

Original languageEnglish
Pages (from-to)331-360
Number of pages30
JournalDuke Mathematical Journal
Volume146
Issue number2
DOIs
StatePublished - 1 Feb 2009
Externally publishedYes

ASJC Scopus subject areas

  • General Mathematics

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