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.