TIME-DEPENDENT CORRELATION-FUNCTIONS IN A ONE-DIMENSIONAL ASYMMETRIC EXCLUSION PROCESS

We continue our studies [J. Stat. Phys. 71, 485 (1993)] of a one-dimensional anisotropic exclusion process with parallel dynamics describing particles moving to the right on a chain of L sites. Instead of considering periodic boundary conditions with a defect, as in our studies, we study open boundary conditions with injection of particles with rate alpha at the origin and absorption of particles with rate beta at the boundary. We construct the steady state and compute the density profile as a function of alpha and beta. In the large-L limit we find a high-density phase (alpha > beta) and a low-density phase (alpha < beta). In both phases, the density distribution along the chain approaches its respective constant bulk value exponentially on a length scale xi. They are separated by a phase-transition line where xi diverges and where the density increases linearly with the distance from the origin. Furthermore, we present exact expressions for all equal-time n-point density correlation functions and for the time-dependent two-point function in the steady state. We compare our results with predictions from local dynamical scaling and discuss some conjectures for other exclusion models.