Eur. Phys. J. B 65, 257-264 (2008)
https://doi.org/10.1140/epjb/e2008-00330-7

Interacting random walkers and non-equilibrium fluctuations

¹ Dipartimento di Fisica, Università di Parma, Viale G.P. Usberti n.7/A (Parco Area delle Scienze) 43100 Parma, Italy
² Theoretische Polymerphysik, Universität Freiburg, Hermann-Herder-Str. 3, 79104 Freiburg, Germany
³ CNR-INFM (Parma), Viale G.P. Usberti n.7/A (Parco Area delle Scienze) 43100 Parma, Italy
⁴ INFN, gruppo collegato di Parma, Viale G.P. Usberti n.7/A (Parco Area delle Scienze) 43100 Parma, Italy

Corresponding author: ^a mario.casartelli@fis.unipr.it

Received: 29 April 2008
Published online: 22 August 2008

Abstract

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.