, Volume 88, Issue 3, pp 387-397

Schrödinger operators with an electric field and random or deterministic potentials

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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.
Partially supported by N.S.F. Grant MCS-82-02045
Partially supported by N.S.F. Grant MCS-81-20833
Communicated by T. Spencer