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Relaxation of initial spatially unhomogeneous states of phonon gases scattered by point mass defects embedded in isotropic media

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Zeitschrift für Physik B Condensed Matter

Abstract

The Cauchy problem for the Boltzmann-Peierls equation describing the rarefied gas of acoustic phonons scattered by point mass defects embedded in an isotropic medium is studied. The equation for the Fourier-Laplace transform of the distribution function obtained from the Boltzmann-Peierls equation is solved. The singularities of the Fourier-Laplace transform of the distribution function are investigated. The explicit time dependence of the Fourier transform is established. The crossover from kinetic to diffusive behaviour and the long-time asymptotics of the distribution function is studied. The spectral decomposition of the collision operator is obtained and several lowest order terms of the Chapman-Enskog series are derived. For comparison the suitable results for two dimensional isotropic media are listed.

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Authors and Affiliations

  1. Institute of Theoretical Physics, University of Wroclaw, ul. Cybulskiego 36, PL-50-205, Wroclaw, Poland

    Cz. Jasiukiewicz & T. Paszkiewicz

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  1. Cz. Jasiukiewicz
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  2. T. Paszkiewicz
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Jasiukiewicz, C., Paszkiewicz, T. Relaxation of initial spatially unhomogeneous states of phonon gases scattered by point mass defects embedded in isotropic media. Z. Physik B - Condensed Matter 77, 209–218 (1989). https://doi.org/10.1007/BF01313665

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  • DOI: https://doi.org/10.1007/BF01313665

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