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Localization for random Schrödinger operators with correlated potentials

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Abstract

We prove localization at high disorder or low energy for lattice Schrödinger operators with random potentials whose values at different lattice sites are correlated over large distances. The class of admissible random potentials for our multiscale analysis includes potentials with a stationary Gaussian distribution whose covariance functionC(x,y) decays as |x−y|−θ, where θ>0 can be arbitrarily small, and potentials whose probability distribution is a completely analytical Gibbs measure. The result for Gaussian potentials depends on a multivariable form of Nelson's best possible hypercontractive estimate.

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Author notes

  1. Henrique von Dreifus

    Present address: Instituto de Mathematica e Estatistica, Universidade de São Paulo, São Paulo, S.P., Brazil

Authors and Affiliations

  1. Department of Physics, Princeton University, 08544, Princeton, NJ, USA

    Henrique von Dreifus

  2. Department of Mathematics, University of California at Irvine, 92717, Irvine, CA, USA

    Abel Klein

Authors
  1. Henrique von Dreifus
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  2. Abel Klein
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Additional information

Communicated by T. Spencer

Partially supported by the NSF under grant PHY8515288

Partially supported by the NSF under grant DMS8905627

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von Dreifus, H., Klein, A. Localization for random Schrödinger operators with correlated potentials. Commun.Math. Phys. 140, 133–147 (1991). https://doi.org/10.1007/BF02099294

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  • DOI: https://doi.org/10.1007/BF02099294

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