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Approach to Equilibrium in a Microscopic Model of Friction

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Abstract

We consider the time evolution of a disk under the action of a constant force and interacting with a free gas in the mean-field approximation. Letting V 0>0 be the initial velocity of the disk and V ∞>0 its equilibrium velocity, namely the one for which the external field is balanced by the friction force exerted by the background, we show that, if V ∞−V 0 is positive and sufficiently small, then the disk reaches V ∞ with the power law t − (d+2), d=1,2,3 being the dimension of the physical space. The reason for this behavior is the long tail memory due to recollisions. Any Markovian approximation (or simply neglecting the recollisions) yields an exponential approach to equilibrium.

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Authors and Affiliations

  1. Dipartimento di Matematica, Università di Roma `Tor Vergata', via della Ricerca Scientifica, 00133, Roma, Italy

    S. Caprino

  2. Dipartimento di Matematica, Università di Roma `La Sapienza', P.le Aldo Moro 2, 00185, Roma, Italy

    C. Marchioro & M. Pulvirenti

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  1. S. Caprino
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  2. C. Marchioro
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  3. M. Pulvirenti
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Correspondence to S. Caprino.

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Communicated by H. Spohn

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Caprino, S., Marchioro, C. & Pulvirenti, M. Approach to Equilibrium in a Microscopic Model of Friction. Commun. Math. Phys. 264, 167–189 (2006). https://doi.org/10.1007/s00220-006-1542-7

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  • DOI: https://doi.org/10.1007/s00220-006-1542-7

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