One-dimensional partially asymmetric simple exclusion process on a ring with a defect particle

The effect of a moving defect particle for the one-dimensional partially asymmetric simple exclusion process on a ring is considered. The current of the ordinary particles, the speed of the defect particle, and the density profile of the ordinary particles are calculated exactly. The phase diagram for the correlation length is identified. As a by-product, the average and the variance of the particle density of the one-dimensional partially asymmetric simple exclusion process with open boundaries are also computed.