Collective transport of particles in a ''flashing'' periodic potential

We consider the collective motion of finite size Brownian particles induced by a one-dimensional, spatially asymmetric, periodic potential which is turned ''on'' and ''off'' dichotomously. The particles interact through simple hard-core repulsion. We show analytically that this simple system exhibits an interesting collective behavior: (i) the direction of motion can change many times as the density of particles is increased; (ii) close to the maximal density, the average velocity depends on the size of the particles in a very complex way, both in sign and magnitude.