Spontaneous symmetry breaking in a two-lane system with parallel update

Abstract

This paper studies a two-lane totally asymmetric simple exclusion processes (TASEP) with narrow entrances under parallel update. Particles move on two parallel lanes in the opposite directions without lane changing. The narrow entrances are modelled in this way: the entry of a particle is not allowed if the exit site of the other lane is occupied (see also Pronina and Kolomeisky 2007 J. Phys. A: Math. Theor. 40 2275). We mainly focus on the case where particles hop deterministically in the bulk. The phase diagram, bulk density and particle currents are analysed using mean-field approximation. It is shown that there are two symmetry breaking phases, and one of them (i.e., asymmetric low density/low-density phase) occupies only a line in the phase diagram. A multi-stable phenomenon is also observed. Monte Carlo simulations are carried out and the simulation results deviate from the mean-field prediction, because correlations are not considered in mean-field calculation. A seesaw phase is reproduced when α = 1. The results are also compared with that obtained from the two-lane system with random update. Finally, preliminary simulation results where particles hop with the rate q < 1 in the bulk are reported and it is shown that the introduction of stochastic hopping changes the phase diagram structure.