On the Absolutely Continuous Spectrum of Stark Operators.

The stability of the absolutely continuous spectrum of the one-dimensional Stark operator H = - ^d²/_dx² - Fx, under perturbations of the potential is discussed. The focus is on proving this stability under minimal assumptions on smoothness of the perturbation. A general criterion is presented together with some applications. These include the case of periodic perturbations where we show that any perturbation v ϵ L₁ (T) ∩ H^-1/2(T) preserves the a.c. spectrum. [ABSTRACT FROM AUTHOR]