Non-universal coarsening and universal distributions in far-from equilibrium systems

TL;DR

This paper investigates anomalous coarsening in far-from-equilibrium one-dimensional systems through simulations and analytic methods, revealing universal distribution tails and scaling laws influenced by cluster breakup dynamics.

Contribution

It introduces a minimal exclusion model with specific mechanisms, derives scaling laws for domain growth, and uncovers universal distribution tails that differ from independent cluster predictions.

Findings

Domain growth follows x ~ (epsilon t)^z with z=1/(2+alpha)

Cluster length distributions have universal tails ~ exp(-y^{3/2})

Simulation confirms scaling laws and universal distribution behavior

Abstract

Anomalous coarsening in far-from equilibrium one-dimensional systems is investigated by simulation and analytic techniques. The minimal hard core particle (exclusion) models contain mechanisms of aggregated particle diffusion, with rates epsilon<<1, particle deposition into cluster gaps, but suppressed for the smallest gaps, and breakup of clusters which are adjacent to large gaps. Cluster breakup rates vary with the cluster length x as kx^alpha. The domain growth law x ~ (epsilon t)^z, with z=1/(2+alpha) for alpha>0, is explained by a scaling picture, as well as the scaling of the density of double vacancies (at which deposition and cluster breakup are allowed) as 1/[t(epsilon t)^z]. Numerical simulations for several values of alpha and epsilon confirm these results. An approximate factorization of the cluster configuration probability is performed within the master equation resulting from the mapping to a column picture. The equation for a one-variable scaling function explains the above results. The probability distributions of cluster lengths scale as P(x)= 1/(epsilon t)^z g(y), with y=x/(epsilon t)^z. However, those distributions show a universal tail with the form g(y) ~ exp(-y^{3/2}), which disagrees with the prediction of the independent cluster approximation. This result is explained by the connection of the vacancy dynamics with the problem of particle trapping in an infinite sea of traps and is confirmed by simulation.