On the mobility of a one-dimensional damped Frenkel-Kontorova chain: Commensurate versus incommensurate

The mobility of a one-dimensional damped Frenkel-Kontorova chain under a de driving force is studied numerically and analytically For the commensurate case, the particles in the chain me synchronized st high driving force. For the incommensurate chain, a single mode solution dominates st high mobility regime. We are able to calculate the mobilities for both the cases analytically, and a good agreement with numerical results is found. The mobility hysteresis for the incommensurate chain is explained by the existence of two branches of physical solutions, and transitions occur when one of them breaks up.