Superdiffusive Heat Transport in a class of Deterministic One-Dimensional Many-Particle Lorentz gases - Condensed Matter > Statistical MechanicsReportar como inadecuado




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Abstract: We study heat transport in a one-dimensional chain of a finite number $N$ ofidentical 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 continuousversion of this model was derived in a scaling regime where the scatteringprobability of the tracers is $\gamma\sim1-N$, corresponding to the Grad limit.A Boltzmann type equation describing the transport of heat was obtained. Inthis paper, we show numerically that the Boltzmann description obtained in\cite{CE08} is indeed a bona fide limit of the particle model. Furthermore, wealso study the heat transport of the model when the scattering probability isone, corresponding to deterministic dynamics. At a coarse grained level themodel behaves as a persistent random walker with a broad waiting timedistribution and strong correlations associated to the deterministicscattering. We show, that, in spite of the absence of global conservedquantities, the model leads to a superdiffusive heat transport.Ref CE08 P. Collet and J. P. Eckmann. A model of heat conduction. ArXiv0804:3025, 2008.



Autor: Pierre Collet, Jean-Pierre Eckmann, Carlos~Mejia-Monasterio

Fuente: https://arxiv.org/







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