Extended states in a lifshitz tail regime for random Schrödinger operators on trees

Michael Aizenman, Simone Warzel

Research output: Contribution to journalArticle

24 Scopus citations

Abstract

We resolve an existing question concerning the location of the mobility edge for operators with a hopping term and a random potential on the Bethe lattice. The model has been among the earliest studied for Anderson localization, and it continues to attract attention because of analogies which have been suggested with localization issues for many particle systems. We find that extended states appear through disorder enabled resonances well beyond the energy band of the operator's hopping term. For weak disorder this includes a Lifshitz tail regime of very low density of states.

Original languageEnglish (US)
Article number136804
JournalPhysical review letters
Volume106
Issue number13
DOIs
StatePublished - Mar 29 2011

All Science Journal Classification (ASJC) codes

  • Physics and Astronomy(all)

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