2 research outputs found
Interacting Random Walkers and Non-Equilibrium Fluctuations
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.Comment: 8 pages, 7 figure