PHASE-SEPARATION AND COARSENING IN ONE-DIMENSIONAL DRIVEN DIFFUSIVE SYSTEMS - LOCAL DYNAMICS LEADING TO LONG-RANGE HAMILTONIANS

A driven system of three species of particles diffusing on a ring is s tudied in detail. The dynamics is local and conserves the three densit ies. A simple argument suggesting that the model should phase separate and break the translational symmetry is given. We show that for the s pecial case where the three densities are equal the model obeys detail ed balance, and the steady-state distribution is governed by a Hamilto nian with asymmetric long-range interactions. This provides an explici t demonstration of a simple mechanism for breaking of ergodicity in on e dimension. The steady state of finite-size systems is studied using a generalized matrix product ansatz. The coarsening process leading to phase separation is studied numerically and in a mean-field model. Th e system exhibits slow dynamics due to trapping in metastable states w hose number is exponentially large in the system size. The typical dom ain size is shown to grow logarithmically in time. Generalizations to a larger number of species are discussed.