01-180 I. Rodnianski, W. Schlag

Classical and quantum scattering for a class of long range random potentials (522K, Postscript) May 16, 01

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Abstract. We prove an almost sure existence of the modified wave operators for a class of Schr\"odinger operators with random long range potentials. The assumed decay of the potential at infinity puts it beyond the threshold of the standard class of long range potentials as described in the work of Buslaev-Matveev, Alsholm-Kato, and H\"ormander. We develop an approach which relies on the averaging of the potential over the classical {\it random} trajectories. As a byproduct we also obtain a classical scattering picture for the correspoding classical hamiltonians.

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