Spontaneous symmetry breaking in totally asymmetric simple exclusion processes on two intersected lattices

This paper studies totally asymmetric simple exclusion processes (TASEPs) on two intersected lattices. Three different models are introduced: model A for molecular motor motion, and models B and C for vehicle traffic. Extensive Monte Carlo simulations are carried out. Phase diagrams and density profiles of the three models are investigated. It is shown that phase diagrams of all the three models are divided into three regions. The phase boundaries are calculated by an approximate mean-field approach. It is found that the analytic solutions are in good agreement with the results of Monte Carlo simulations. For models B and C, spontaneous symmetry breaking is identified. The particle density histograms and qualitative domain-wall explanation are presented to describe the spontaneous symmetry breaking phenomenon. Finally, in model C, the effect of lane-changing probability p on spontaneous symmetry breaking is investigated. A threshold of p for the occurrence of symmetry breaking is obtained.