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

doi:10.1088/1674-1056/acc058

中国物理B ›› 2023, Vol. 32 ›› Issue (7): 70504-070504.doi: 10.1088/1674-1056/acc058

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

Bo Tian(田波)^†, Wan-Qiang Wen(文万强), A-Min Li(李阿敏), and Ping Xia(夏萍)

School of Engineering, Anhui Agricultural University, Hefei 230036, China

收稿日期:2022-11-02 修回日期:2023-02-20 接受日期:2023-03-02 出版日期:2023-06-15 发布日期:2023-06-29
通讯作者: Bo Tian E-mail:tianbo@ahau.edu.cn
基金资助:
Project supported by the National Natural Science Foundation of China (Grant No. 11802003).

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

Bo Tian(田波)^†, Wan-Qiang Wen(文万强), A-Min Li(李阿敏), and Ping Xia(夏萍)

School of Engineering, Anhui Agricultural University, Hefei 230036, China

Received:2022-11-02 Revised:2023-02-20 Accepted:2023-03-02 Online:2023-06-15 Published:2023-06-29
Contact: Bo Tian E-mail:tianbo@ahau.edu.cn
Supported by:
Project supported by the National Natural Science Foundation of China (Grant No. 11802003).

摘要/Abstract

摘要： 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.

关键词: asymmetric simple exclusion process, spontaneous symmetry breaking, simple mean-field analysis, cluster mean-field analysis

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 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.

Key words: asymmetric simple exclusion process, spontaneous symmetry breaking, simple mean-field analysis, cluster mean-field analysis

中图分类号: (Phase transitions: general studies)

05.70.Fh

02.50.Ey (Stochastic processes) 05.60.Cd (Classical transport)

Bo Tian(田波), Wan-Qiang Wen(文万强), A-Min Li(李阿敏), and Ping Xia(夏萍). Symmetry phases of asymmetric simple exclusion processes on two lanes with an intersection[J]. 中国物理B, 2023, 32(7): 70504-070504.

Bo Tian(田波), Wan-Qiang Wen(文万强), A-Min Li(李阿敏), and Ping Xia(夏萍). Symmetry phases of asymmetric simple exclusion processes on two lanes with an intersection[J]. Chin. Phys. B, 2023, 32(7): 70504-070504.

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

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

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