Pierre Collet, Jean-Pierre Eckmann, Carlos Mejia-Monasterio
Superdiffusive Heat Transport in a Class of Deterministic One-Dimensional Many-Particle Lorentz Gases
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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,
\cite{CE08}, a spatially continuous version of this model was
derived in a scaling regime where the scattering probability of the tracers is $\gamma\sim1/N$, corresponding to the
Grad limit.
A Boltzmann type equation
describing the transport of heat was obtained. In this paper, we show
numerically that the Boltzmann
description obtained in
\cite{CE08} is indeed a bona fide limit of the particle model.
Furthermore, we also study the heat
transport of the model when the scattering probability is one,
corresponding to deterministic dynamics.
At a coarse grained level the model behaves as a
persistent random walker with a broad waiting time distribution and
strong correlations
associated to the deterministic scattering. We show, that, in spite
of the absence of
global conserved quantities, the model leads to a superdiffusive heat
transport.