A Multi-Species Asymmetric Exclusion Model with an Impurity

Abstract

A multi-species generalization of the Asymmetric Simple Exclusion Process (ASEP) has been considered in the presence of a single impurity on a ring. The model describes particles hopping in one direction with stochastic dynamics and hard core exclusion condition. The ordinary particles hop forward with their characteristic hopping rates and fast particles can overtake slow ones with a relative rate. The impurity, which is the slowest particle in the ensemble of particles on the ring, hops in the same direction of the ordinary particles with its intrinsic hopping rate and can be overtaken by ordinary particles with a rate which is not necessarily a relative rate. We will show that the phase diagram of the model can be obtained exactly. It turns out that the phase structure of the model depends on the density distribution function of the ordinary particles on the ring so that it can have either four phases or only one. The mean speed of impurity and also the total current of the ordinary particles are explicitly calculated in each phase. Using Monte Carlo simulation, the density profile of the ordinary particles is also obtained. The simulation data confirm all of the analytical calculations.