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Effects of junctional correlations in the totally asymmetric simple exclusion process on random regular networks

We investigate the totally asymmetric simple exclusion process on closed and directed random regular networks, which is a simple model of active transport in the one-dimensional segments coupled by junctions. By a pair mean-field theory and detailed numerical analyses, it is found that the correlations at junctions induce two notable deviations from the simple mean-field theory which neglects these correlations: (1) the narrower range of particle density for phase coexistence and (2) the algebraic decay of density profile with exponent $1/2$ even outside the maximal-current phase. We show that these anomalies are attributable to the effective slow bonds formed by the network junctions.