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New Characterizations of the Region of Complete Localization for Random Schrödinger Operators

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Abstract

We study the region of complete localization in a class of random operators which includes random Schrödinger operators with Anderson-type potentials and classical wave operators in random media, as well as the Anderson tight-binding model. We establish new characterizations or criteria for this region of complete localization, given either by the decay of eigenfunction correlations or by the decay of Fermi projections. (These are necessary and sufficient conditions for the random operator to exhibit complete localization in this energy region.) Using the first type of characterization we prove that in the region of complete localization the random operator has eigenvalues with finite multiplicity.

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Authors and Affiliations

  1. Département de Mathématiques, Université de Cergy-Pontoise, Site de Saint-Martin, 2 avenue Adolphe Chauvin, Cergy-Pontoise cedex, 95302, France

    Francois Germinet

  2. Department of Mathematics, University of California, Irvine, CA, 92697-3875, USA

    Abel Klein

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  1. Francois Germinet
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  2. Abel Klein
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Correspondence to Francois Germinet.

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Germinet, F., Klein, A. New Characterizations of the Region of Complete Localization for Random Schrödinger Operators. J Stat Phys 122, 73–94 (2006). https://doi.org/10.1007/s10955-005-8068-9

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