Directed transport of Brownian particles in a double symmetric potential
  We investigate the dynamics of Brownian particles in internal state- dependent symmetric and periodic potentials. Although no space or time symmetry of the Hamiltonian is broken, we show that directed transport can appear. We demonstrate that the directed motion is induced by breaking the symmetry of the transition rates between the potentials when these are spatially shifted. Finally, we discuss the possibility of realizing our model in a system of cold particles trapped in optical lattices. 
Laurent Sanchez-Palencia