Schrödinger operators with an electric field and random or deterministic potentials

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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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