Interacting Random Walkers and Non-Equilibrium Fluctuations

Details Interacting Random Walkers and Non-Equilibrium Fluctuations Interacting Random Walkers and Non-Equilibrium Fluctuations

2008-09-30

arxiv.org/abs/0809.5244v1

The European Physical Journal B 65 2 (2008) 257-264

Physics

Condensed Matter

Statistical Mechanics

8 pages, 7 figures

Scientific paper

10.1140/epjb/e2008-00330-7

We introduce a model of interacting Random Walk, whose hopping amplitude depends on the number of walkers/particles on the link. The mesoscopic counterpart of such a microscopic dynamics is a diffusing system whose diffusivity depends on the particle density. A non-equilibrium stationary flux can be induced by suitable boundary conditions, and we show indeed that it is mesoscopically described by a Fourier equation with a density dependent diffusivity. A simple mean-field description predicts a critical diffusivity if the hopping amplitude vanishes for a certain walker density. Actually, we evidence that, even if the density equals this pseudo-critical value, the system does not present any criticality but only a dynamical slowing down. This property is confirmed by the fact that, in spite of interaction, the particle distribution at equilibrium is simply described in terms of a product of Poissonians. For mesoscopic systems with a stationary flux, a very effect of interaction among particles consists in the amplification of fluctuations, which is especially relevant close to the pseudo-critical density. This agrees with analogous results obtained for Ising models, clarifying that larger fluctuations are induced by the dynamical slowing down and not by a genuine criticality. The consistency of this amplification effect with altered coloured noise in time series is also proved.

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