Weakening interaction suppresses spontaneous symmetry breaking in two-channel asymmetric exclusion processes

Abstract

This paper has studied spontaneous symmetry breaking (SSB) phenomenon in two types of two-channel asymmetric simple exclusion processes (ASEPs). One common feature of the two systems is that interactions for each species of particle happen at only one site, and the system reduces to two independent ASEPs when interaction vanishes. It is shown that with the weakening of interaction, the SSB is suppressed. More interestingly, the SSB disappears before the interaction is eliminated. Our work thus indicates that local interaction has to be strong enough to produce SSB. The mean-field analysis has been carried out, and the results are consistent with the simulation ones.

Asymmetric simple exclusion processes with complex lattice geometries: A review of models and phenomena

“…The SSB can also be observed in a system in which the interactions for each species of particle happen at only one site in the two-channel TASEP with two species of particles. [38] It is shown that with the weakening of interaction, the SSB is suppressed. Authors in Ref.…”

“…Authors in Ref. [38] reported an interesting phenomenon that the SSB disappears before the interaction is eliminated. However, the reason has not been given in Ref.…”

“…However, the reason has not been given in Ref. [38]. The SSB was studied in the TASEP with two intersected channels in Ref.…”

Spurious symmetry-broken phase in a bidirectional two-lane ASEP with narrow entrances

“…Particles move along the lattice obeying a hard-core exclusion principle. This simple model can reproduce many non-equilibrium phenomena such as spontaneous symmetry breaking, [30][31][32][33][34][35][36][37][38][39][40][41][42] boundary-induced [43][44][45] and bulk-induced [46] phase transitions, phase separation and condensation, [47][48][49][50][51] shock formation, [11,12,46,52] and so on. Thus, as Blythe and Evans [4] pointed out, "our interest in the ASEP lies in its having acquired the status of a fundamental model of nonequilibrium statistical physics in its own right in much the same way that the Ising model has become a paradigm for equilibrium critical phenomena.…”

“…[30,31] From then on, the phenomenon in ASEP models has gained a great deal of attention. [32][33][34][35][36][37][38][39][40][41][42] However, the mechanism of this phenomenon is still not well understood.…”