Lifschitz Tails for Random Schrödinger Operator in Bernoulli Distributed Potentials

Michael Bishop, Vita Borovyk, Jan Wehr

Research output: Contribution to journalArticle

Abstract

This paper presents an elementary proof of Lifschitz tail behavior for random discrete Schrödinger operators with a Bernoulli-distributed potential. The proof approximates the low eigenvalues by eigenvalues of sine waves supported where the potential takes its lower value. This is motivated by the idea that the eigenvectors associated to the low eigenvalues react to the jump in the values of the potential as if the jump were infinite.

Original languageEnglish (US)
Pages (from-to)151-162
Number of pages12
JournalJournal of Statistical Physics
Volume160
Issue number1
DOIs
StatePublished - Jul 23 2015

Keywords

  • Bernoulli random variables
  • Lifschitz tail
  • Random Schrödinger operator

ASJC Scopus subject areas

  • Statistical and Nonlinear Physics
  • Mathematical Physics

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