Realização do processo de exclusão totalmente assimétrico de um sistema de partículas brownianas interagentes

Abstract

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. In the one-dimensional TASEP with open boundaries, particles are insertedat the leftmost site at rate a, hop to the right at unit rate (as long as the target site is empty), and are removed at the rightmost site at rate ß. This model exhibits three distinct phases in the a¡ß plane. Our study of a continuous-space model is motivated by recent experiments on colloidalparticles in optical tweezer arrays, which offer the promise of a laboratory realization of the TASEP. The external potential in our model 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. Ashort-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, as in the lattice model. We study the model via numerical integration ofthe Langevin equation and dynamic Monte Carlo simulations. Our results for the density profile and current indicate that the continuous-space model exhibits phase transitions analogous to the continuous and discontinuous transitions observed in the lattice model