On the Mobility of a One-Dimensional Damped Frenkel-Kontorova Chain: Commensurate Versus Incommensurate**The project supported in part by the grants from the Hong Kong Research Grants Council (RGC) and the Hong Kong Baptist University Faculty Research Grant (FRG), Zhang's work is also partly supported by National Natural Science Foundation of China, the Education Ministry of the State Council through the Foundation

Abstract

The mobility of a,one-dimensional damped fienkel-Kontorova chain under a dcdriving force is studied numerically and analytically. For the commensurate case, the particles in the chain are synchronized at high driving force. For the incommensurate chain, a single mode solution dominates at 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.