A matrix ansatz for the diffusion of an impurity in the asymmetric exclusion process

We study the fluctuations of the position of an impurity in the asymmetric exclusion process on a ring with an arbitrary number of particles and holes. The steady state of this model is exactly known and four different phases appear in the limit of a large system. We calculate the diffusion constant of the impurity by using a matrix product method and also obtain a representation for unequal time correlation functions. We show that our results found by the matrix ansatz agree with those obtained previously by the Bethe ansatz.