Please wait a minute...
Chin. Phys. B, 2023, Vol. 32(7): 070504    DOI: 10.1088/1674-1056/acc058
GENERAL Prev   Next  

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
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.
Keywords:  asymmetric simple exclusion process      spontaneous symmetry breaking      simple mean-field analysis      cluster mean-field analysis  
Received:  02 November 2022      Revised:  20 February 2023      Accepted manuscript online:  02 March 2023
PACS:  05.70.Fh (Phase transitions: general studies)  
  02.50.Ey (Stochastic processes)  
  05.60.Cd (Classical transport)  
Fund: Project supported by the National Natural Science Foundation of China (Grant No. 11802003).
Corresponding Authors:  Bo Tian     E-mail:  tianbo@ahau.edu.cn

Cite this article: 

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 2023 Chin. Phys. B 32 070504

[1] Macdonald C T, Gibbs J H and Pipkin A C 1968 Biopolymers 6 1
[2] Chou T and Lakatos G 2004 Phys. Rev. Lett. 93 198101
[3] Schütz G M 1999 Europhys. Lett. 48 623
[4] Widom B, Viovy J L and Defontaines A D 1991 J. Phys. I France 1 1759
[5] Chou T 1998 Phys. Rev. Lett. 80 85
[6] Chowdhury D, Santen L and Schadschneider A 2000 Phys. Rep. 329 199
[7] Helbing D 2001 Rev. Mod. Phys. 73 1067
[8] Arita C, Foulaadvand M E and Santen L 2017 Phys. Rev. E 95 032108
[9] Xiao S, Cai J J and Liu F 2009 Chin. Phys. B 18 4613
[10] Xiao S, Cai J J, Liu F and Liu M Z 2010 Chin. Phys. B 19 090202
[11] Liu M Z, Li S D and Wang R L 2012 Chin. Phys. B 21 090510
[12] Liu M Z, Li S D and Wang R L 2012 Comput. Phys. Commun. 183 316
[13] Derrida B, Evans M R, Hakim V and Pasquier V 1993 J. Phys. A: Math. Gen. 24 1493
[14] Schütz G M and Domany E 1993 J. Stat. Phys. 72 227
[15] Evans M R, Foster D P, Godreche C and Mukamel D 1995 Phys. Rev. Lett. 74 208
[16] Yuan Y M, Jiang R, Wang R, Wu Q S and Zhang J Q 2008 J. Phys. A: Math. Gen. 41 035003
[17] Tian B, Jiang R, Hu M B, Ding Z J and Jia B 2020 Physica A 541 123542
[18] Tian B, Jiang R, Hu M B, Ding Z J and Jia B 2020 Europhys. Lett. 128 40005
[19] Kolomeisky A B 1998 J. Phys. A: Math. Gen. 31 1153
[20] Tian B, Xia P, Liu L, Wu M R and Guo S Y 2020 Chin. Phys. B 29 050505
[21] Evans M R, Foster D P, Godreche C and Mukamel D 1995 Phys. Rev. Lett. 74 208
[22] Pronina E and Kolomeisky A B 2007 J. Phys. A: Math. Gen. 40 2275
[23] Popkov V, Evans M R and Mukamel D 2008 J. Phys. A: Math. Theor. 41 432002
[24] de Queiroz S L A and Stinchcombe R B 2019 Phys. Rev. E 100 012141
[25] Jindal A, Kolomeisky A B and Gupta A K 2020 J. Stat. Mech.: Theory Exp. 2020 113202
[26] Pal B and Gupta A K 2021 J. Phys. A: Math. Gen. 54 405002
[27] Tian B, Li A M, Wen W Q and Xia P 2022 Chaos Soliton Fract. 165 112713
[28] Derrida B 1998 Phys. Rep. 301 65
[29] Schütz G M 2000 Integrable Stochastic Many-Body Systems in Phase Transitions and Critical Phenomena vol. 19 Domb C and Lebowitz J (eds) (London: Academic)
[1] Existence of spontaneous symmetry breaking in two-lane totally asymmetric simple exclusion processes with an intersection
Bo Tian(田波), Ping Xia(夏萍), Li Liu(刘莉), Meng-Ran Wu(吴蒙然), Shu-Yong Guo(郭树勇). Chin. Phys. B, 2020, 29(5): 050505.
[2] Spurious symmetry-broken phase in a bidirectional two-lane ASEP with narrow entrances
Bo Tian(田波), Rui Jiang(姜锐), Mao-Bin Hu(胡茂彬), Bin Jia(贾斌). Chin. Phys. B, 2017, 26(2): 020503.
[3] Asymmetric simple exclusion processes with complex lattice geometries: A review of models and phenomena
Liu Ming-Zhe (刘明哲), Li Shao-Da (李少达), Wang Rui-Li. Chin. Phys. B, 2012, 21(9): 090510.
[4] Spontaneous symmetry breaking vacuum energy in cosmology
Zhou Kang(周康), Yue Rui-Hong(岳瑞宏), Yang Zhan-Ying(杨战营), and Zou De-Cheng(邹德成) . Chin. Phys. B, 2012, 21(7): 079801.
[5] Theoretical investigation of total-asymmetric simple exclusion processes with attachment and detachment
Xiao Song(肖松), Liu Ming-Zhe(刘明哲), Shang Jing(商晶), and Wang Hua(王华) . Chin. Phys. B, 2012, 21(2): 020514.
[6] Spontaneous symmetry breaking of a Bose–Fermi mixture in a two-dimensional double-well potential
Wang Yuan-Sheng(王元生), Yan Pei-Gen(颜培根), Li Bin(李彬), and Liu Xue-Shen(刘学深) . Chin. Phys. B, 2012, 21(1): 010309.
[7] Effect of unequal injection rates on asymmetric exclusion processes with junction
Xiao Song(肖松), Liu Ming-Zhe(刘明哲), Wang Jian-Jun(王建军), and Wang Hua(王华). Chin. Phys. B, 2011, 20(6): 060509.
[8] Effect of unequal injection rates and different hopping rates on asymmetric exclusion processes with junction
Xiao Song(肖松), Cai Jiu-Ju(蔡九菊), Liu Fei(刘飞), and Liu Ming-Zhe(刘明哲). Chin. Phys. B, 2010, 19(9): 090202.
[9] Successive defects asymmetric simple exclusion processes with particles of arbitrary size
Cai Jiu-Ju(蔡九菊),Xiao Song(肖松), Wang Ruo-Hui(王若翚), and Liu Fei(刘飞) . Chin. Phys. B, 2009, 18(12): 5097-5102.
[10] Zone inhomogeneity with the random asymmetric simple exclusion process in a one-lane system
Xiao Song(肖松), Cai Jiu-Ju(蔡九菊), and Liu Fei(刘飞) . Chin. Phys. B, 2009, 18(11): 4613-4621.
No Suggested Reading articles found!