Bethe ansatz solution for a defect particle in the asymmetric exclusion process

The asymmetric exclusion process on a ring in one dimension is considered w ith a single defect particle. The steady state has previously been solved b y a matrix product method. Here we use the Bethe ansatz to solve exactly fo r the long time limit behaviour of the generating function of the distance travelled by the defect particle. This allows us to recover steady state pr operties known from the matrix approach such as the velocity, and obtain ne w results such as the diffusion constant of the defect particle. In the cas e where the defect particle is a second-class particle we determine the lar ge deviation function and show that in a certain range the distribution of the distance travelled about the mean is Gaussian. Moreover, the variance ( diffusion constant) grows as L-1/2 where L is the system size. This behavio ur can be related to the superdiffusive spreading of excess mass fluctuatio ns on an infinite system. In the case where the defect particle produces a shock, our expressions for the velocity and the diffusion constant coincide with those calculated previously for an infinite system by Ferrari and Fon tes.