| Identifiant de l'article : |
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hal-00461276, version 1 |
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arXiv:1003.1011 |
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| Domaine : |
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Physique/Matière Condensée/Mécanique statistique
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| Titre : |
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Approach to a stationary state in an external field |
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| Auteur(s) : |
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Angel Alastuey1, Jaroslaw Piasecki2 |
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| Laboratoire : |
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Phys-ENS - Laboratoire de Physique de l'ENS Lyon |
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| 2 : |
Institute of Theoretical Physics |
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| Résumé : |
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We study relaxation towards a stationary out of equilibrium state by analizing a one-dimensional stochastic process followed by a particle accelerated by an external field and propagating through a thermal bath. The effect of collisions is described within Botlzmann's kinetic theory. We present analytical solutions for the Maxwell gas and for the very hard particle model. The exponentially fast relaxation of the velocity distribution toward the stationary form is demonstrated. In the reference frame moving with constant drift velocity the hydrodynamic diffusive mode is shown to govern the distribution in the position space. We show that the exact value of the diffusion coefficient for any value of the field is correctly predicted by Green-Kubo autocorrelation formula generalized to the stationary state. |
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Langue du texte
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Anglais |
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| Mots Clés : |
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stationary state – out-of-equilibrium – relaxation processes – hydrodynamic mode – diffusion – Green-Kubo formula |
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| Classification : |
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PACS numbers : 05-30.-d, 05-70.Ce, 52.25.Kn |
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