Totally asymmetric exclusion process with long-range hopping

Details Totally asymmetric exclusion process with long-range hopping Totally asymmetric exclusion process with long-range hopping

2006-10-18

arxiv.org/abs/cond-mat/0610510v1

Phys. Rev. E 74, 051104 (2006)

Physics

Condensed Matter

Statistical Mechanics

10 pages, 9 figures

Scientific paper

10.1103/PhysRevE.74.051104

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 $p_l\sim 1/l^{\sigma+1}$ is studied by Monte Carlo simulations and the domain-wall approach. For $\sigma>1$ the standard TASEP phase diagram is recovered, but the density profiles near the transition lines display new features when $1<\sigma<2$. 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 $\sigma$-dependent exponent. Within the $\sigma \leq 1$ regime, where the transitions are found to be absent, analytical results in the continuum mean-field approximation are derived in the limit $\sigma=-1$.

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