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Normal Transport Properties in a Metastable Stationary State for a Classical Particle Coupled to a Non-Ohmic Bath

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Abstract

We study the Hamiltonian motion of an ensemble of unconfined classical particles driven by an external field F through a translationally-invariant, thermal array of monochromatic Einstein oscillators. The system does not sustain a stationary state, because the oscillators cannot effectively absorb the energy of high speed particles. We nonetheless show that the system has at all positive temperatures a well-defined low-field mobility μ over macroscopic time scales of order exp (c/F), during which it finds itself in a metastable stationary state. The mobility is independent of F at low fields, and related to the zero-field diffusion constant D through the Einstein relation. The system therefore exhibits normal transport even though the bath obviously has a discrete frequency spectrum (it is simply monochromatic) and is therefore highly non-Ohmic. Such features are usually associated with anomalous transport properties.

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Authors and Affiliations

  1. Laboratoire Paul Painlevé, CNRS, UMR 8524 et UFR de Mathématiques, Université des Sciences et Technologies de Lille, 59655, Villeneuve d’Ascq Cedex, France

    P. Lafitte & S. De Bièvre

  2. Equipe-Projet SIMPAF, Centre de Recherche INRIA Futurs, Parc Scientifique de la Haute Borne, 40, avenue Halley, B.P. 70478, 59658, Villeneuve d’Ascq Cedex, France

    P. Lafitte & S. De Bièvre

  3. Department of Physics, Missouri University of Science and Technology, Rolla, MO, 65409, USA

    P. E. Parris

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  1. P. Lafitte
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  2. P. E. Parris
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  3. S. De Bièvre
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Correspondence to S. De Bièvre.

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Lafitte, P., Parris, P.E. & De Bièvre, S. Normal Transport Properties in a Metastable Stationary State for a Classical Particle Coupled to a Non-Ohmic Bath. J Stat Phys 132, 863–879 (2008). https://doi.org/10.1007/s10955-008-9590-3

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  • DOI: https://doi.org/10.1007/s10955-008-9590-3

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