Giant enhancement of diffusion and particle selection in rocked periodic potentials

We investigate the motion of an overdamped Brownian particle in a periodic potential with weak thermal noise and a time-periodic unbiased (i.e. [F(t)]= 0) external driving force F(t). By introducing appropriate "waiting-periods", where F(t) vanishes, an arbitrarily strong enhancement of diffusion in a symmetric potential is possible. In asymmetric periodic potentials (ratchets) the net flux of particles can be directed in both directions, even in the absence of thermal noise. For finite temperatures we observe and explain additional, pure-noise-induced flux reversal phenomena.