Phase transition in the two-component symmetric exclusion process with openboundaries

Abstract

We study single-file diffusion in an open system with two speciesA, B of particles. At the boundaries we assume different reservoir densities which drive thesystem into a non-equilibrium steady state. As a model we use a one-dimensionaltwo-component simple symmetric exclusion process with two different hopping ratesDA, DB and open boundaries. For investigating the dynamics in the hydrodynamic limit we derive asystem of coupled non-linear diffusion equations for the coarse-grained particledensities. The relaxation of the initial density profile is analysed by numericalintegration. Exact analytical expressions are obtained for the self-diffusion coefficients,which turn out to be length dependent, and for the stationary solution. In thesteady state we find a discontinuous boundary-induced phase transition as thetotal exterior density gradient between the system boundaries is varied. At oneboundary a boundary layer develops inside which the current flows against thelocal density gradient. Generically the width of the boundary layer and the bulkdensity profiles do not depend on the two hopping rates. At the phase transitionline, however, the individual density profiles depend strongly on the ratioDA/DB. Dynamic Monte Carlo simulations confirm our theoretical predictions.