Time-dependent correlation functions in a one-dimensional asymmetric exclusion process

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Abstract
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 α at the origin and absorption of particles with rate β at the boundary. We construct the steady state and compute the density profile as a function of α and β. In the large-L limit we find a high-density phase (α>β) and a low-density phase (α<β). In both phases, the density distribution along the chain approaches its respective constant bulk value exponentially on a length scale ξ. They are separated by a phase-transition line where ξ 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.
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