Phase transitions in an exactly soluble one-dimensional exclusion process

Abstract

We consider an exclusion process, with particles injected with rate $α$ at the origin and removed with rate $β$ at the right boundary of a one-dimensional chain of sites. The particles are allowed to hop onto unoccupied sites, to the right only. For the special case of $α=β=1$ the model was solved previously by Derrida et al. Here we extend the solution to general $α,β$. The phase diagram obtained from our exact solution differs from the one predicted by the mean field approximation.