Abstract: Two-lane totally asymmetric simple exclusion process (TASEP) with narrow entrances was studied. The N-cluster mean field analysis was carried out for spontaneous symmetric breaking, in which correlation of 2N sites was considered. The analysis indicates that asymmetric LD/LD(low density/low density) phase does not exist. With increase of N, the analytical results are getting closer to the Monte Carlo simulation ones. In addition, it was found that the boundaries between the phases all exhibit exponential change, which enables us to predict the boundaries in the exact solution, and it was shown that the predicted results are in good agreement with the large size simulation ones. The spontaneous symmetric breaking exists when interaction between particles represented by parameter p is strong enough. It was found that the maximum values of entrance rate of asymmetric HD/LD(high density/low density) phase obey exponential decay with increase of p, and the critical value beyond which the asymmetric HD/LD phase disappears can be obtained in every cluster mean field analysis. What’s more, the critical values exhibit exponential increase with increase of N, and the exact solution of the critical value was also predicted. It was shown that the predicted critical value is also in good agreement with that obtained from simulations.

Key words: spontaneous symmetry breaking, simple mean field analysis, cluster mean field analysis, asymmetric simple exclusion process