Existence of spontaneous symmetry breaking in two-lane totally asymmetric simple exclusion processes with an intersection*

Tian, Bo; Xia, Ping; Liu, Li; Wu, Meng-Ran; Guo, Shu-Yong

doi:10.1088/1674-1056/ab820e

Cited by 1 publication

(2 citation statements)

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“…Then, studies of ASEP with single lane have been generalized to ASEP with multilane which exhibits a variety of cooperative phenomena, such as shock formation, [12,13] phase separation, [14,15] and spontaneous symmetry breaking (SSB). [16][17][18][19][20] SSB is an interesting phenomenon in which symmetric conditions of the dynamic processes lead to existence of phases with broken symmetries. The phenomenon was first observed in the bridge model in which two species of particles move in the opposite directions in the single lane.…”

Section: Introductionmentioning

confidence: 99%

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

Tian

Wen

et al. 2023

Chinese Phys. B

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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.

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Section: Introductionmentioning

confidence: 99%

“…Motivated by this, cluster mean field analysis is often adopted, the correlation of sites is considered, and it performs much better than the simple mean field analysis. [17,18,20,24,25,27] Yuan et al have investigated totally asymmetric simple exclusion processes on two intersected lattices. [16] Three mod-els are studied.…”

Section: Introductionmentioning

confidence: 99%