Anderson localization for Bernoulli and other singular potentials View Full Text


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Article Info

DATE

1987-03

AUTHORS

Rene Carmona, Abel Klein, Fabio Martinelli

ABSTRACT

We prove exponential localization in the Anderson model under very weak assumptions on the potential distribution. In one dimension we allow any measure which is not concentrated on a single point and possesses some finite moment. In particular this solves the longstanding problem of localization for Bernoulli potentials (i.e., potentials that take only two values). In dimensions greater than one we prove localization at high disorder for potentials with Hölder continuous distributions and for bounded potentials whose distribution is a convex combination of a Hölder continuous distribution with high disorder and an arbitrary distribution. These include potentials with singular distributions. We also show that for certain Bernoulli potentials in one dimension the integrated density of states has a nontrivial singular component. More... »

PAGES

41-66

References to SciGraph publications

  • 1986-06. A supersymmetric transfer matrix and differentiability of the density of states in the one-dimensional Anderson model in COMMUNICATIONS IN MATHEMATICAL PHYSICS
  • 1985-12. Anderson localization for multi-dimensional systems at large disorder or large energy in COMMUNICATIONS IN MATHEMATICAL PHYSICS
  • 1986-12. A rigorous replica trick approach to Anderson localization in one dimension in COMMUNICATIONS IN MATHEMATICAL PHYSICS
  • 1984-06. On absence of diffusion near the bottom of the spectrum for a random Schrödinger operator onL2(ℝ)+ in COMMUNICATIONS IN MATHEMATICAL PHYSICS
  • 1985. Products of Random Matrices with Applications to Schrödinger Operators in NONE
  • 1984. Repartition d'etat d'un operateur de Schrödinger aleatoire Distribution empirique des valeurs propres d'une matrice de Jacobi in PROBABILITY MEASURES ON GROUPS VII
  • 1985-03. Harmonic analysis on SL(2,R) and smoothness of the density of states in the one-dimensional Anderson model in COMMUNICATIONS IN MATHEMATICAL PHYSICS
  • 1985-03. Constructive proof of localization in the Anderson tight binding model in COMMUNICATIONS IN MATHEMATICAL PHYSICS
  • 1980-06. Spectral properties of disordered systems in the one-body approximation in COMMUNICATIONS IN MATHEMATICAL PHYSICS
  • 1985-11. Anderson localization for one- and quasi-one-dimensional systems in JOURNAL OF STATISTICAL PHYSICS
  • 1980-12. Sur le spectre des opérateurs aux différences finies aléatoires in COMMUNICATIONS IN MATHEMATICAL PHYSICS
  • 1981-03. Bounds on the density of states in disordered systems in ZEITSCHRIFT FÜR PHYSIK B CONDENSED MATTER
  • 1985-09. Remark on the absence of absolutely continuous spectrum ford-dimensional Schrödinger operators with random potential for large disorder or low energy in COMMUNICATIONS IN MATHEMATICAL PHYSICS
  • 1983-06. Absence of diffusion in the Anderson tight binding model for large disorder or low energy in COMMUNICATIONS IN MATHEMATICAL PHYSICS
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    http://scigraph.springernature.com/pub.10.1007/bf01210702

    DOI

    http://dx.doi.org/10.1007/bf01210702

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