Sliding dynamics of the Frenkel-Kontorova model

We investigate the dynamics of the Frenkel-Kontorova model with inertia and damping under a uniform driving force. We consider the dependence of the velocity-force characteristic, and the corresponding sliding states on the damping: In the overdamped limit the asymptotic solution with nonzero sliding velocity is unique and periodic. Periodic solutions and their stability can also be calculated for decreasing damping, where the dynamics is dominated by resonance effects of the underlying potential with the phonon modes of the chain. The asymptotic velocity is not unique, leading to hysteresis in the velocity-force characteristic. In addition to periodic sliding states, which lose stability for decreasing damping, quasiperiodic or spatio-temporal chaotic behavior occurs.