On the sliding dynamics of the Frenkel-Kontorova model

We study the underdamped dynamics of the Frenkel-Kontorova model (i.e., a harmonic chain in a spatially periodic potential) driven by a uniform force. The behavior is dominated by the resonant excitation of phonon modes due to the periodic potential. We find periodic, quasiperiodic, and chaotic sliding states. The velocity-force characteristic shows hysteresis between these different states. Furthermore we investigate the pinning-depinning transition which becomes a first order transition in the underdamped regime.