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Superdiffusive heat transport in a class of deterministic one-dimensional many-particle Lorentz gases

Published inJournal of statistical physics, vol. 136, p. 331-347
Publication date2009
Abstract

We study heat transport in a one-dimensional chain of a finite number N of identical cells, coupled at its boundaries to stochastic particle reservoirs. At the center of each cell, tracer particles collide with fixed scatterers, exchanging momentum. In a recent paper (Collet and Eckmann in Commun. Math. Phys. 287:1015, 2009), a spatially continuous version of this model was derived in a scaling regime where the scattering probability of the tracers is γ∼1/N, corresponding to the Grad limit. A Boltzmann-like equation describing the transport of heat was obtained. In this paper, we show numerically that the Boltzmann description obtained in Collet and Eckmann (Commun. Math. Phys. 287:1015, 2009) is indeed a bona fide limit of the particle model. Furthermore, we study the heat transport of the model when the scattering probability is 1, corresponding to deterministic dynamics. Thought as a lattice model in which particles jump between different scatterers the motion is persistent, with a persistence probability determined by the mass ratio among particles and scatterers, and a waiting time probability distribution with algebraic tails. We find that the heat and particle currents scale slower than 1/N, implying that this model exhibits anomalous heat and particle transport.

Keywords
  • Boltzmann equation
  • Non-equilibrium
  • Steady state
  • Heat conduction
  • Anomalous transport
  • Superdiffusion
  • Infinite invariant measures
Citation (ISO format)
COLLET, Pierre, ECKMANN, Jean-Pierre, MEJIA-MONASTERIO, Carlos. Superdiffusive heat transport in a class of deterministic one-dimensional many-particle Lorentz gases. In: Journal of statistical physics, 2009, vol. 136, p. 331–347. doi: 10.1007/s10955-009-9783-4
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ISSN of the journal0022-4715
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