Dynamics of an incommensurate harmonic chain

The dynamics of a one-dimensional harmonic chain in a strong, incommensurate, sinusoidal potential and a uniform force $F$ is investigated. A threshold force $F_t$ exists, above which the mean velocity $\overline{v}$ of the chain satisifes $\overline{v}\propto {(F-F_t)}^{\zeta }$ where $\zeta =0.68\mathrm{}\pm 0.05$. We present evidence that no coherent velocity oscillations occur in the infinite system. The possible relevance of this work to experimental observations of charge-density waves is discussed.