Particle separation by external fields on periodic surfaces

Particles moving on perfect periodic surfaces under the influence of external forces may move along directions that deviate from that of the force. We briefly recall previous results for transport of particles on surfaces with periodic traps or periodic obstacles driven by a constant external force, and present new results for particles moving in a harmonic periodic potential. The sorting properties are explored as a function of a number of control parameters, specifically the friction, force amplitude and direction, temperature, and lattice constants.