Totally asymmetric exclusion process with long-range hopping

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 $\sigma=-1$.