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

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 the other particle can move forward with rate p in the sites of downstream segments. The parameter p can represent the rate of slowing 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 analyze the system, and the system is divided into four independent segments. It is found that the analytical results deviate from the simulation ones, especially when p is small. In addition, the inexsitence of SSB can only be explained qualitatively. Motivated by this, we carry out the cluster mean field analysis in which correlation of five sites is considered. 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.

Automated summary

This paper investigates two-lane asymmetric simple exclusion processes (ASEPs) with an intersection. Monte Carlo simulations are conducted to study the system's behavior. The results show that there are three symmetric phases and no spontaneous symmetry breaking (SSB) in the system. Initially, a simple mean field approach is used to analyze the system, but it deviates from the simulation results, especially for small values of the parameter p. Therefore, a cluster mean field analysis is conducted, considering the correlation of five sites. The analysis demonstrates that densities of the two upstream segments are equal, indicating the absence of SSB. The cluster mean field analysis performs better than the simple mean field analysis.