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

TL;DR

This paper studies a two-species symmetric exclusion process with open boundaries, revealing a boundary-induced phase transition characterized by a boundary layer and density profile changes, supported by analytical and simulation results.

Contribution

It derives coupled nonlinear diffusion equations for a two-component exclusion process and uncovers a novel boundary-induced phase transition with detailed analytical and numerical analysis.

Findings

Discontinuous phase transition in steady state density profiles.

Boundary layer formation with current flowing against the density gradient.

Density profiles depend on hopping rate ratio at the transition line.

Abstract

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.