Schroedinger operators withan electric field and random or deterministic potential

We prove that the Schrödinger operator H=−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.