engleski

Scaling in the exclusion process with long-range hopping

We investigate the exclusion process in which particles may jump any distance l with the probability that decays as l^&#8722; (1+\sigma). Besides the localization of the domain-wall at first-order phase transition, previous results have shown a change in the continuous phase transition to the maximum-current phase. In particular, the exponent of the algebraic decay of the density profile differs from the short-range value 1/2 in the region 1<\sigma<2, where its dependence on \sigma was given by the conjecture based on numerical simulations. In the present work, we obtain the exact value of this exponent from a hydrodynamic equation for the density profile in the mean-field approximation. For \sigma>2, this equation is given by the viscous Burgers' equation of the short-range case, but the usual diffusion term of this equation is replaced by the fractional one for 1<\sigma<2. The nonlocal character of this term induces the external field that creates and annihilates particles in the bulk, similar to the exclusion process with Langmuir kinetics, but with site-dependent rates that influence the scaling behavior in the maximum-current phase. In case of the translationally invariant system, the equation can be mapped onto the fractional Kardar-Parisi-Zhang equation which predicts the value of the dynamical exponent z = min{;\sigma, 3/2}; in agreement with the results of our numerical simulations on the half-filled chain with periodic boundary conditions.

ASEP; asymmetric exclusion process; phase transitions out of equilibrium

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