TASEP of interacting particles of arbitrary size

Abstract

A mean-field description of the stationary state behaviour of interacting k-mers performing totally asymmetric exclusion processes (TASEP) on an open lattice segment is presented employing the discrete Takahashi formalism. It is shown how the maximal current and the phase diagram, including triple-points, depend on the strength of repulsive and attractive interactions. We compare the mean-field results with Monte Carlo simulation of three types interacting k-mers: monomers, dimers and trimers. (a) We find that the Takahashi estimates of the maximal current agree quantitatively with those of the Monte Carlo simulation in the absence of interaction as well as in both the the attractive and the strongly repulsive regimes. However, theory and Monte Carlo results disagree in the range of weak repulsion, where the Takahashi estimates of the maximal current show a monotonic behaviour, whereas the Monte Carlo data show a peaking behaviour. It is argued that the peaking of the maximal current is due to a correlated motion of the particles. In the limit of very strong repulsion the theory predicts a universal behavior: th maximal currents of k-mers correspond to that of non-interacting -mers; (b) Monte Carlo estimates of the triple-points for monomers, dimers and trimers show an interesting general behaviour : (i) the phase boundaries and for entry and exit current, respectively, as function of interaction strengths show maxima for whereas exhibit minima at the same strength; (ii) in the attractive regime, however, the trend is reversed (). The Takahashi estimates of the triple-point for monomers show a similar trend as the Monte Carlo data except for the peaking of ; for dimers and trimers, however, the Takahashi estimates show an opposite trend as compared to the Monte Carlo data.

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