Classical and Quantum Scattering for a Class of Long Range Random Potentials

We prove an almost sure existence of the modified wave operators for a class of Schrödinger operators with random long range potentials. The assumed decay of potential at infinity places it beyond the threshold of the standard class of long range potentials as described in the work of Buslaev-Matveev, Alsholm-Kato, and Hörmander. We develop an approach to quantum scattering which relies on averaging of potential over classical random trajectories. We also establish classical scattering for corresponding classical hamiltonians.