Absolutely continuous spectrum of perturbed Stark operators

We prove new results on the stability of the absolutely continuous spectrum for perturbed Stark operators with decaying or satisfying certain smoothness assumption perturbation. We show that the absolutely continuous spectrum of the Stark operator is stable if the perturbing potential decays at the rate $(1+x)^{-\frac{1}{3}-\epsilon}$ or if it is continuously differentiable with derivative from the H\"older space $C_{\alpha}(R),$ with any $\alpha>0.$