Spontaneous symmetry breaking and periodic structure in a multilane system

We study a multilane totally asymmetric simple exclusion process (TASEP) with narrow entrances under parallel update. The narrow entrances are modeled in this way: the entry of a particle is not allowed if the exit site of the previous lane is occupied. It is shown the results depend on the number of lanes, n. If n is an even number, the results are essentially the same as n=2: two symmetry-breaking phases-i.e., a high-density-low-density (HD-LD) phase and an asymmetric low-density-low-density phase-are identified. In contrast, if n is an odd number, a periodic structure is observed and the period is found to be proportional to the lane number n and system size L. It is also found when the injection rate α=1 that the seesaw phase observed in the case of n=2 disappears and the HD-LD phase or symmetric LD phase appears. Some mean-field calculations are also presented. We show that it is not possible to have high densities in two successive lanes and also not possible to have high density in one lane and low densities in all other lanes. For odd n, we have obtained the period T and it is in good agreement with simulations for a small removal rate β, but deviates from simulation results for large β because correlation is neglected in the mean-field approximation.