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Kinetic limit for a harmonic chain with a conservative Ornstein-Uhlenbeck stochastic perturbation

  • * Corresponding author: Tomasz Komorowski

    * Corresponding author: Tomasz Komorowski 
Both authors acknowledge the support of the Polish National Science Center grant UMO-2012/07/B/ST1/03320
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  • We consider a one dimensional infinite chain of harmonic oscillators whose dynamics is weakly perturbed by a stochastic term conserving energy and momentum and whose evolution is governed by an Ornstein-Uhlenbeck process. We prove the kinetic limit for the Wigner functions corresponding to the chain. This result generalizes the results of [7] obtained for a random momentum exchange that is of a white noise type. In contrast with [7] the scattering term in the limiting Boltzmann equation obtained in the present situation depends also on the dispersion relation.

    Mathematics Subject Classification: Primary: 82C44; Secondary: 82C20, 82C70.


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