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arXiv · 0804.4094

Scaling properties of the asymmetric exclusion process with long-range hopping

J. Szavits-Nossan·K. Uzelac
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Abstract

The exclusion process in which particles may jump any distance l>=1 with the probability that decays as l^-(1+sigma) is studied from coarse-grained equation for density profile in the limit when the lattice spacing goes to zero. For 1<sigma<2, the usual diffusion term of this equation is replaced by the fractional one, which affects dynamical-scaling properties of the late-time approach to the stationary state. When applied to an open system with totally asymmetric hopping, this approach gives two results: first, it accounts for the sigma-dependent exponent that characterizes the algebraic decay of density profile in the maximum-current phase for 1<sigma<2, and second, it shows that in this region of sigma the exponent is of the mean-field type.

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J. Szavits-Nossan, K. Uzelac. 2008-04-25. Scaling properties of the asymmetric exclusion process with long-range hopping. https://doi.org/10.1103/physreve.77.051116

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