Schrödinger operators with an electric field and random or deterministic potentials
- Cite this article as:
- Bentosela, F., Carmona, R., Duclos, P. et al. Commun.Math. Phys. (1983) 88: 387. doi:10.1007/BF01213215
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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.