An exactly soluble non-equilibrium system: The asymmetric simple exclusion process

A number of exact results have been obtained recently for the one-dimensional asymmetric simple exclusion process, a model of particles which hop to their right at random times, on a one-dimensional lattice, provided that the target site is empty. Using either a matrix form for the steady-state weights or the Bethe ansatz, several steady-state properties can be calculated exactly: the current, the density profile for open boundary conditions, the diffusion constant of a tagged particle. The matrix form of the steady state can be extended to calculate exactly the steady state of systems of two species of particles and shock profiles. (C) 1998 Elsevier Science B.V. All rights reserved.