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Totally asymmetric exclusion process with long-range hopping

J. Szavits-Nossan·K. Uzelac
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Abstract

Generalization of the one-dimensional totally asymmetric exclusion process (TASEP) with open boundary conditions in which particles are allowed to jump $l$ sites ahead with the probability $p_l\sim 1/l^{σ+1}$ is studied by Monte Carlo simulations and the domain-wall approach. For $σ>1$ the standard TASEP phase diagram is recovered, but the density profiles near the transition lines display new features when $1<σ<2$. At the first-order transition line, the domain-wall is localized and phase separation is observed. In the maximum-current phase the profile has an algebraic decay with a $σ$-dependent exponent. Within the $σ\leq 1$ regime, where the transitions are found to be absent, analytical results in the continuum mean-field approximation are derived in the limit $σ=-1$.

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J. Szavits-Nossan, K. Uzelac. 2006-10-18. Totally asymmetric exclusion process with long-range hopping. https://doi.org/10.1103/physreve.74.051104

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