Symmetry phases of asymmetric simple exclusion processes on two lanes with an intersection

Abstract

This paper studies two-lane asymmetric simple exclusion processes (ASEPs) with an intersection. In the upstream segments of the intersection, one particle can move to the next site with rate $1$ if the site is empty, and one particle can move forward with rate $p$ in the sites of downstream segments. The parameter $p$ can represent the rate of slowing down of motion, and the parameter is introduced to investigate spontaneous symmetry breaking (SSB) phenomenon. Extensive Monte Carlo simulations are carried out. It is shown that three symmetric phases exist and the SSB does not exist in the system. Simple mean field approach in which correlation of sites is ignored is firstly adopted to analyse the system, and the system is divided into four independent segments. It is found that the analytical results deviate the simulation ones, especially when $p$ is small. In addition, the inexsitence of SSB can only be explained qualitatively. Motivated by this, cluster mean field analysis in which correlation of five sites is considered is also carried out. It is shown that densities of the two upstream segments are equal, which demonstrates that the SSB does not exist. It is also shown that, as expected, the cluster mean field analysis performs much better than the simple mean field analysis.