Exact diffusion constant for one-dimensional exclusion models

For the ID fully asymmetric exclusion model with open boundary conditions, we calculate xactly the fluctuations of the current of particles. The method used is an extension of a matrix technique developed recently to describe the equal-time steady-state properties for open boundary conditions and the diffusion constant for particles on a ring. We show how the fluctuations of the current are related to non-equal-time correlations. In the thermodynamic l mit, our results agree with recent results of Ferrari and Fontes obtained by working directly in the infinite system. We also show that the fluctuations of the current become singular when the system undergoes a phase transition with discontinuities along the first-order transition line