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September 2004 The Quantum Scattering Limit for a Regularized Wigner Equation
Benoît Perthame, Lenya Ryzhik
Methods Appl. Anal. 11(3): 447-464 (September 2004).

Abstract

We consider a regularized Wigner equation with an oscillatory kernel, the regularization acts in the space variable to damp high frequencies. The oscillatory kernel is directly derived from the Schr\"odinger equation with an oscillatory potential. The problem therefore contains three scales, $\eps$ the oscillation length, $\theta$ the regularization parameter, $\delta$ the potential lattice.

We prove that the homogenized limit (as $\eps$ vanishes) of this equation is a scattering equation with discrete jumps. As $\delta$ vanishes, the discrete scattering kernel boils down to a standard regular scattering kernel. As $\theta$ vanishes we recover the quantum scattering operator with collisions preserving energy sphere.

Citation

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Benoît Perthame. Lenya Ryzhik. "The Quantum Scattering Limit for a Regularized Wigner Equation." Methods Appl. Anal. 11 (3) 447 - 464, September 2004.

Information

Published: September 2004
First available in Project Euclid: 11 May 2006

zbMATH: 1092.81026
MathSciNet: MR2214687

Rights: Copyright © 2004 International Press of Boston

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Vol.11 • No. 3 • September 2004
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