Impurity-induced shocks in the asymmetric exclusion process with long-range hopping

Details Impurity-induced shocks in the asymmetric exclusion process with long-range hopping Impurity-induced shocks in the asymmetric exclusion process with long-range hopping

2009-11-27

arxiv.org/abs/0911.5280v1

J. Stat. Mech. (2009) P12019

Physics

Condensed Matter

Statistical Mechanics

13 pages, 7 figures, to appear in JSTAT

Scientific paper

10.1088/1742-5468/2009/12/P12019

We consider the totally asymmetric simple exclusion process (TASEP) on the periodic chain in the presence of a single impurity site that is inaccessible to other particles and therefore acts as a static defect. Particles are allowed to advance any distance l \geq 1 on the right with the probability that decays as l^-(1+sigma), where sigma > 1. Despite the long range of hopping, we find the same type of phase transition that occurs in the standard short-range TASEP with a defect site where defect induces a macroscopic shock in the stationary state. In particular, our model displays two main features characteristic of the short-range TASEP with defect site: a growth of the shock width with system size L as L^(1/2) or L^(1/3), depending on the existence of the particle-hole symmetry, and the power-law decay in density profiles of the shock phase. However, unlike the profiles in the short-range case, we find that the latter are well reproduced by the mean-field approximation, which enables us to derive the analytical expression for sigma-dependent exponent nu = sigma-1 of this power-law decay and the point sigma_c = 4/3 at which the transition takes place.

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