Synchronized shocks in an inhomogeneous exclusion process
Theoretische Physik, Universität des Saarlandes - 66041 Saarbrücken, Germany
Received: 27 August 2015
Accepted: 9 November 2015
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, , 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 . 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.
PACS: 05.40.-a – Fluctuation phenomena, random processes, noise, and Brownian motion / 02.50.Ey – Stochastic processes
© EPLA, 2015