Phase transition in the two-component symmetric exclusion process with open boundaries

Details Phase transition in the two-component symmetric exclusion process with open boundaries Phase transition in the two-component symmetric exclusion process with open boundaries

2007-05-04

arxiv.org/abs/0705.0596v1

Physics

Condensed Matter

Statistical Mechanics

26 pages, 6 figures

Scientific paper

We consider single-file diffusion in an open system with two species $A,B$ of particles. At the boundaries we assume different reservoir densities which drive the system into a non-equilibrium steady state. As a model we use an one-dimensional two-component simple symmetric exclusion process with two different hopping rates $D_A,D_B$ and open boundaries. For investigating the dynamics in the hydrodynamic limit we derive a system of coupled non-linear diffusion equations for the coarse-grained particle densities. The relaxation of the initial density profile is analyzed by numerical integration. Exact analytical expressions are obtained for the self-diffusion coefficients, which turns out to be length-dependent, and for the stationary solution. In the steady state we find a discontinuous boundary-induced phase transition as the total exterior density gradient between the system boundaries is varied. At one boundary a boundary layer develops inside which the current flows against the local density gradient. Generically the width of the boundary layer and the bulk density profiles do not depend on the two hopping rates. At the phase transition line, however, the individual density profiles depend strongly on the ratio $D_A/D_B$. Dynamic Monte Carlo simulation confirm our theoretical predictions.

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