Smoothness of correlations in the Anderson model at strong disorder

Jean V. Bellissard, Peter D. Hislop

Research output: Contribution to journalArticlepeer-review

4 Scopus citations

Abstract

We study the higher-order correlation functions of covariant families of observables associated with random Schrödinger operators on the lattice in the strong disorder regime. We prove that if the distribution of the random variables has a density analytic in a strip about the real axis, then these correlation functions are analytic functions of the energy outside of the planes corresponding to coincident energies. In particular, this implies the analyticity of the density of states, and of the current-current correlation function outside of the diagonal. Consequently, this proves that the current-current correlation function has an analytic density outside of the diagonal at strong disorder.

Original languageEnglish
Pages (from-to)1-26
Number of pages26
JournalAnnales Henri Poincare
Volume8
Issue number1
DOIs
StatePublished - Feb 2007

Bibliographical note

Funding Information:
∗ Partially supported by NSF Grant 0300398. † Partially supported by NSF Grant 0503784.

ASJC Scopus subject areas

  • Statistical and Nonlinear Physics
  • Nuclear and High Energy Physics
  • Mathematical Physics

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