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

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.

10 pages, 8 figures

References in corpus (16)

• Universality classes in nonequilibrium lattice systems
• Phase transitions in an exactly soluble one-dimensional exclusion process
• Phase Coexistence in Driven One Dimensional Transport
• Bethe Ansatz Solution of the Asymmetric Exclusion Process with Open Boundaries
• The Totally Asymmetric Simple Exclusion Process with Langmuir Kinetics
• Shock formation in an exclusion process with creation and annihilation
• Exact solution of a cellular automaton for traffic
• Exact Spectral Gaps of the Asymmetric Exclusion Process with Open Boundaries
• Continuous Limit of Discrete Systems with Long-Range Interaction
• Exact Stationary State for an ASEP with Fully Parallel Dynamics
• Dynamic correlation functions and Boltzmann Langevin approach for driven one dimensional lattice gas
• Dynamics of an exclusion process with creation and annihilation
• Density Profile of the One-Dimensional Partially Asymmetric Simple Exclusion Process with Open Boundaries
• Growing Surfaces with Anomalous Diffusion - Results for the Fractal Kardar-Parisi-Zhang Equation
• Totally asymmetric exclusion process with long-range hopping
• Renormalized field theory and particle density profile in driven diffusive systems with open boundaries

Cited by in corpus (6)

• Slow to fast infinitely extended reservoirs for the symmetric exclusion process with long jumps
• Nonlocal Asymmetric exclusion process on a ring and conformal invariance
• Impurity-induced shocks in the asymmetric exclusion process with long-range hopping
• Condensation transition in a model with attractive particles and non-local hops
• Asymmetric simple exclusion process in one-dimensional chains with long-range links
• Absence of phase coexistence in disordered exclusion processes with bypassing