Interacting Random Walkers and Non-Equilibrium Fluctuations

TL;DR

This paper introduces a model of interacting random walkers with density-dependent diffusivity, revealing that interactions amplify fluctuations without true criticality, and characterizing the non-equilibrium behavior and fluctuation dynamics.

Contribution

It presents a novel interacting random walk model with density-dependent hopping, analyzing non-equilibrium fluxes, fluctuations, and the absence of true criticality despite dynamical slowing down.

Findings

Density-dependent diffusivity leads to non-equilibrium stationary flux.

Interactions amplify fluctuations near pseudo-critical density.

No genuine criticality observed; fluctuations linked to slowing down.

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.