Asymmetric simple exclusion process in one-dimensional chains with long-range links

We study the boundary-driven asymmetric simple exclusion process(ASEP) in a one-dimensional chain with long-range links. Shortcuts are added to a chain by connecting pL different pairs of sites selected randomly where L and p denote the chain length and the shortcut density, respectively. Particles flow into a chain at one boundary at a rate α and out of a chain at the other boundary at a rate β, while they hop inside a chain via nearest-neighbor bonds and long-range shortcuts. Without shortcuts, the model reduces to the boundary-driven ASEP in a one-dimensional chain which displays the low-density, high-density and maximal-current phases. Shortcuts lead to a drastic change. Numerical simulation studies suggest that there emerge three phases: an empty phase with ρ = 0, a jammed phase with ρ = 1 and a shock phase with 0 < ρ < 1 where ρ is the mean particle density. The shock phase is characterized with a phase separation between an empty region and a jammed region with a localized shock between them. The mechanism for the shock formation and the nonequilibrium phase transition are explained by an analytical theory based on a mean-field approximation and an annealed approximation.