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Lifschitz Tails for Random Schrödinger Operator in Bernoulli Distributed Potentials

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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.

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Acknowledgments

The authors would like to thank R. Sims, L. Friedlander, and K.McLaughlin, A. Fedorenk for useful discussions. M. Bishop and J. Wehr were partly supported by NSF Grant DMS 0623941.

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Authors and Affiliations

  1. Department of Mathematics, University of California, Davis, Davis, CA, 95616, USA

    Michael Bishop

  2. Department of Mathematics, University of Cincinnati, Cincinnati, OH, 45221-0025, USA

    Vita Borovyk

  3. Department of Mathematics, University of Arizona, Tucson, AZ, 85721-0089, USA

    Jan Wehr

Authors
  1. Michael Bishop
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  2. Vita Borovyk
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  3. Jan Wehr
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Correspondence to Michael Bishop.

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Bishop, M., Borovyk, V. & Wehr, J. Lifschitz Tails for Random Schrödinger Operator in Bernoulli Distributed Potentials. J Stat Phys 160, 151–162 (2015). https://doi.org/10.1007/s10955-015-1242-9

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  • DOI: https://doi.org/10.1007/s10955-015-1242-9

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