Unlocking mechanism in the ac dynamics of the Frenkel-Kontorova model

The dissipative dynamics of commensurate structures of the one-dimensional Frenkel-Kontorova model submitted to dc and ac forces is studied. The average velocity varies with the average external force as a staircase (dynamical mode locking). We characterize the unlocking transition as a transition from temporal periodicity to quasiperiodicity by using standard tools of the theory of dynamical systems. This transition is phenomenologically described as the generation of coherent, time-localized, and regularly-distributed increases of the particle velocities (instantons), which carry out a topological charge, the origin of which is the discrete character of the symmetry group of transformations of the locked steady state.