Fluctuations of solutions to Wigner equation with an Ornstein-Uhlenbeck potential

Tomasz Komorowski; Lenya Ryzhik

doi:10.3934/dcdsb.2012.17.871

Article Contents

2012, Volume 17, Issue 3: 871-914. Doi: 10.3934/dcdsb.2012.17.871

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Fluctuations of solutions to Wigner equation with an Ornstein-Uhlenbeck potential

Tomasz Komorowski^1, and
Lenya Ryzhik^2,

1.
Institute of Mathematics, UMCS 20-031, Lublin, Poland and IMPAN 00-956 Warsaw
2.
Department of Mathematics, Stanford University, Stanford, CA 94305

Received: June 30, 2010

Revised: January 31, 2011

Published: April 2012

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Abstract

We consider energy fluctuations for solutions of the Schrödinger equation with an Ornstein-Uhlenbeck random potential when the initial data is spatially localized. The limit of the fluctuations of the Wigner transform satisfies a kinetic equation with random initial data. This result generalizes that of [12] where the random potential was assumed to be white noise in time.

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Mathematics Subject Classification: Primary: 60H25; Secondary: 35Q40.

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