Communications in Mathematical Physics

, Volume 88, Issue 3, pp 387–397

Schrödinger operators with an electric field and random or deterministic potentials

  • F. Bentosela
  • R. Carmona
  • P. Duclos
  • B. Simon
  • B. Souillard
  • R. Weder
Article

DOI: 10.1007/BF01213215

Cite this article as:
Bentosela, F., Carmona, R., Duclos, P. et al. Commun.Math. Phys. (1983) 88: 387. doi:10.1007/BF01213215

Abstract

We prove that the Schrödinger operatorH=−d2/dx2+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.

Copyright information

© Springer-Verlag 1983

Authors and Affiliations

  • F. Bentosela
    • 1
  • R. Carmona
    • 2
  • P. Duclos
    • 3
    • 1
  • B. Simon
    • 4
  • B. Souillard
    • 5
  • R. Weder
    • 6
  1. 1.Département de Physique de l'Université de Luminy Marseille, and Centre de Physique Théorique, CNRSMarseilleFrance
  2. 2.Department of MathematicsUniversity of California at IrvineIrvineUSA
  3. 3.Département de MathématiquesUniversité de Toulon et du VarLa Garde
  4. 4.Department of Mathematics and PhysicsCalifornia Institute of TechnologyPassadenaUSA
  5. 5.Centre de Physique Théorique, Ecole PolytechniquePalaiseauFrance
  6. 6.IIMAS, Universidad Nacional Autonoma de MexicoMexico 20 D.F.Mexico

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