Schrödinger operators with an electric field and random or deterministic potentials

Communications in Mathematical Physics volume 88, pages387–397(1983)Cite this article

Abstract

We prove that the Schrödinger operatorH=−d 2/dx 2+V(x)+F·x has purely absolutely continuous spectrum for arbitrary constant external fieldF, for a large class of potentials; this result applies to many periodic, almost periodic and random potentials and in particular to random wells of independent depth for which we prove that whenF=0, the spectrum is almost surely pure point with exponentially decaying eigenfunctions.

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Author information

Affiliations

  1. Département de Physique de l'Université de Luminy Marseille, and Centre de Physique Théorique, CNRS, F-13288, Marseille, France

    F. Bentosela & P. Duclos

  2. Department of Mathematics, University of California at Irvine, 92663, Irvine, CA, USA

    R. Carmona

  3. Département de Mathématiques, Université de Toulon et du Var, 83130, La Garde

    P. Duclos

  4. Department of Mathematics and Physics, California Institute of Technology, 91125, Passadena, CA, USA

    B. Simon

  5. Centre de Physique Théorique, Ecole Polytechnique, F-91128, Palaiseau, France

    B. Souillard

  6. IIMAS, Universidad Nacional Autonoma de Mexico, Apartado postal 20-726, Mexico 20 D.F., Mexico

    R. Weder

Authors
  1. F. Bentosela
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  2. R. Carmona
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  3. P. Duclos
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  4. B. Simon
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  5. B. Souillard
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  6. R. Weder
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Additional information

Partially supported by N.S.F. Grant MCS-82-02045

Partially supported by N.S.F. Grant MCS-81-20833

Communicated by T. Spencer

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Bentosela, F., Carmona, R., Duclos, P. et al. Schrödinger operators with an electric field and random or deterministic potentials. Commun.Math. Phys. 88, 387–397 (1983). https://doi.org/10.1007/BF01213215

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Keywords

  • Neural Network
  • Statistical Physic
  • Complex System
  • Nonlinear Dynamics
  • Large Class