Anomalous coarsening in disordered exclusion processes

TL;DR

This paper investigates coarsening dynamics in disordered exclusion processes, revealing distinct time dependencies and unusual exponents across different models through simulations and theoretical analysis.

Contribution

It provides improved phenomenological descriptions and confirms slow coarsening behaviors in disordered exclusion processes with novel findings on dynamical exponents.

Findings

For totally asymmetric process, $\xi(t) o t/(\ln t)^2$ matches simulations.

Partially asymmetric process exhibits logarithmically slow coarsening confirmed by simulations.

Bidirectional two-lane model shows density-dependent dynamical exponents.

Abstract

We study coarsening phenomena in three different simple exclusion processes with quenched disordered jump rates. In the case of the totally asymmetric process, an earlier phenomenological description is improved, yielding for the time dependence of the length scale $\xi(t)\sim t/(\ln t)^2$, which is found to be in agreement with results of Monte Carlo simulations. For the partially asymmetric process, the logarithmically slow coarsening predicted by a phenomenological theory is confirmed by Monte Carlo simulations and numerical mean-field calculations. Finally, coarsening in a bidirectional, two-lane model with random lane-change rates is studied. Here, Monte Carlo simulations indicate an unusual dependence of the dynamical exponent on the density of particles.