Exact Relaxation Dynamics in the Totally Asymmetric Simple Exclusion Process
Abstract
The relaxation dynamics of the one-dimensional totally asymmetric simple exclusion process on a ring is considered in the case of step initial condition. Analyzing the time evolution of the local particle densities and currents by the Bethe ansatz method, we examine their full relaxation dynamics. As a result, we observe peculiar behaviors, such as the emergence of a ripple in the density profile and the existence of the excessive particle currents. Moreover, by making a finite-size scaling analysis of the asymptotic amplitudes of the local densities and currents, we find the scaling exponents with respect to the total number of sites to be -3/2 and -1 respectively.
Cite
@article{arxiv.1201.2749,
title = {Exact Relaxation Dynamics in the Totally Asymmetric Simple Exclusion Process},
author = {Kohei Motegi and Kazumitsu Sakai and Jun Sato},
journal= {arXiv preprint arXiv:1201.2749},
year = {2012}
}
Comments
5 pages, 8 figures, v2: finite-size scaling of asymptotic amplitudes added, v3: minor revision