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Journal of Statistical Physics

, Volume 132, Issue 5, pp 863–879 | Cite as

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

  • P. Lafitte
  • P. E. Parris
  • S. De Bièvre
Article

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.

Keywords

Normal transport Inelastic Lorentz gas Diffusion Mobility 

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© Springer Science+Business Media, LLC 2008

Authors and Affiliations

  1. 1.Laboratoire Paul Painlevé, CNRS, UMR 8524 et UFR de MathématiquesUniversité des Sciences et Technologies de LilleVilleneuve d’Ascq CedexFrance
  2. 2.Equipe-Projet SIMPAFCentre de Recherche INRIA FutursVilleneuve d’Ascq CedexFrance
  3. 3.Department of PhysicsMissouri University of Science and TechnologyRollaUSA

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