Asymmetric Exclusion Process in a System of Interacting Brownian Particles

We study a continuous-space version of the totally asymmetric simple exclusion process (TASEP), consisting of interacting Brownian particles subject to a driving force in a periodic external potential. Particles are inserted at the leftmost site at rate $\alpha$, hop to the right at unit rate, and are removed at the rightmost site at rate $\beta$. Our study is motivated by recent experiments on colloidal particles in optical tweezer arrays. The external potential is of the form generated by such an array. Particles spend most of the time near potential minima, approximating the situation in the lattice gas; a short-range repulsive interaction prevents two particles from occupying the same potential well. A constant driving force, representing Stokes drag on particles suspended in a moving fluid, leads to biased motion. Our results for the density profile and current, obtained via numerical integration of the Langevin equation and dynamic Monte Carlo simulations, indicate that the continuous-space model exhibits phase transitions analogous to those observed in the lattice model. The correspondence is not exact, however, due to the lack of particle-hole symmetry in our model.