Synchronized shocks in an inhomogeneous exclusion process

TL;DR

This paper investigates the dynamic behavior and synchronization of shocks in a four-segment exclusion process with inhomogeneous hopping rates, revealing complex diffusive regimes and introducing new quantitative measures for shock correlation.

Contribution

It provides a detailed analysis of shock dynamics, including diffusion regimes and shock synchronization, in an inhomogeneous exclusion process, extending previous models with new numerical and theoretical insights.

Findings

Shocks exhibit three diffusive regimes with different diffusion coefficients.

Shock correlation and crossover times are quantitatively characterized.

Sub-diffusive behavior proportional to t^{1/2} is observed in certain intervals.

Abstract

We study an exclusion process with 4 segments, which was recently introduced by T Banerjee, N Sarkar and A Basu [J. Stat. Mech. (2015) P01024]. The segments have hopping rates 1, r(<1), 1 and r, respectively. In a certain parameter region, two shocks appear, which are not static but synchronized. We explore dynamical properties of each shock and correlation of shocks, by means of the so-called second-class particle. The mean-squared displacement of shocks has three diffusive regimes, and the asymptotic diffusion coefficient is different from the known formula. In some time interval, it also exhibits sub-diffusion, being proportional to t^{1/2} . Furthermore we introduce a correlation function and a crossover time, in order to quantitatively characterize the synchronization. We numerically estimate the dynamical exponent for the crossover time. We also revisit the 2-segment case and the open boundary condition for comparison.