Interacting random walkers and non-equilibrium fluctuations

• Published in: The European physical journal. B, Condensed matter physics Condensed matter physics, 2008-09, Vol.65 (2), p.257-264
• Main Authors: Agliari, E., Casartelli, M., Vezzani, A.
• Format: Article
• Language: English
• Subjects: Complex Systems; Condensed Matter Physics; Exact sciences and technology; Fluctuation phenomena, random processes, noise, and brownian motion; Fluid- and Aerodynamics; Physics; Physics and Astronomy; Random walks and levy flights; Solid State Physics; Statistical and Nonlinear Physics; Statistical physics, thermodynamics, and nonlinear dynamical systems
• ISSN: 1434-6028; 1434-6036
• DOI: 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.