Abstract
Collective directional transport of particles in symmetric periodic potentials is studied. An example is given to reveal the directed motion of a single particle in a symmetric periodic potential and subject to an asymmetric ac force with zero mean. It is then shown that the asymmetric coupling can give rise to a directed transport. The transport failure (pinning of the lattice) is related to the phase delocalization (crisis) in the circle map. For symmetric couplings, it is found that a train of plane wave can also lead to a directed transport. The mode-locking steps of the transport velocity is found and analyzed. The collective transport can be well optimized by adjusting parameters in the system.
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