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Singularity of the density of states for one-dimensional chains with random couplings

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Abstract

We prove that the density of states for the tight-binding model with off-diagonal disorder under general conditions diverges forR→0 at least as\( \sim \frac{1}{{\left| E \right|(\ln \left| E \right|)^4 }}\). This result is established through the study of the recurrence properties of an associated Markov chain.

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Authors and Affiliations

  1. Instituto di Mathematica, Departimento di Matematica, Università di Bologna, piorza Porta S. Donato, 5, I-40127, Bologna, Italy

    Massimo Campanino

  2. Departimento de Fisica Matematica, IFUSP, P.O. Box 20516, São Paulo, Brazil

    J. Fernando Perez

Authors
  1. Massimo Campanino
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  2. J. Fernando Perez
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Additional information

Communicated by T. Spencer

Partial financial support by GNAFA (CNR)

Partial financial support by CNPq, grant n.303795-77FA

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Campanino, M., Perez, J.F. Singularity of the density of states for one-dimensional chains with random couplings. Commun.Math. Phys. 124, 543–552 (1989). https://doi.org/10.1007/BF01218450

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  • DOI: https://doi.org/10.1007/BF01218450

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