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

Rodnianski, Igor and Schlag, Wilhelm (2003) Classical and Quantum Scattering for a Class of Long Range Random Potentials. International Mathematics Research Notices, 2003 (5). pp. 243-300. ISSN 1073-7928. doi:10.1155/S1073792803201100.

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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.

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Additional Information:© 2003 Hindawi Publishing Corporation. Received 28 January 2002. Revision received 16 June 2002. Accepted October 13, 2002. Communicated by Carlos Kenig. The second author is grateful to Jean Bourgain for his interest and encouragement, and to Alexander Kiselev and Herman Schulz-Baldes for pointing out references [14, 15]. He was partially supported by the National Science Foundation, grant no. DMS-0070538 and a Sloan fellowship.
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Sloan FellowshipUNSPECIFIED
Issue or Number:5
Record Number:CaltechAUTHORS:20111026-142823675
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Official Citation: Igor Rodnianski and Wilhelm Schlag Classical and quantum scattering for a class of long range random potentials Int Math Res Notices (2003) Vol. 2003 243-300 doi:10.1155/S1073792803201100
Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:27461
Deposited By: Ruth Sustaita
Deposited On:26 Oct 2011 21:52
Last Modified:09 Nov 2021 16:49

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