Totally asymmetric exclusion process with long-range hopping

TL;DR

This paper investigates a generalized TASEP model allowing long-range particle jumps with probabilities decaying as a power law, revealing new phase behaviors and density profile features depending on the decay exponent.

Contribution

It introduces a long-range hopping extension to TASEP, analyzes phase diagrams and density profiles, and derives analytical results for the case  using mean-field approximation.

Findings

Standard TASEP phase diagram recovered for 

New features in density profiles for 1<<2

Phase separation observed at first-order transition line

Abstract

Generalization of the one-dimensional totally asymmetric exclusion process (TASEP) with open boundary conditions in which particles are allowed to jump $l$ sites ahead with the probability $p_l\sim 1/l^{\sigma+1}$ is studied by Monte Carlo simulations and the domain-wall approach. For $\sigma>1$ the standard TASEP phase diagram is recovered, but the density profiles near the transition lines display new features when $1<\sigma<2$. At the first-order transition line, the domain-wall is localized and phase separation is observed. In the maximum-current phase the profile has an algebraic decay with a $\sigma$-dependent exponent. Within the $\sigma \leq 1$ regime, where the transitions are found to be absent, analytical results in the continuum mean-field approximation are derived in the limit $\sigma=-1$.