engleski

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

The exclusion process in which particles may jump any distance l &#8805; 1 with the probability that decays as l&#8722; (1+\sigma) is studied from coarse-grained equation for density profile in the limit when 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.

ASEP; asymmetric exclusion process; phase transitions out of equilibrium

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