The dynamical behavior of a weakly damped harmonic chain in a spatially
periodic potential (Frenkel-Kontorova model) under the subject of an external
force is investigated. We show that the chain can be in a spatio-temporally
chaotic state called fluid-sliding state. This is proven by calculating
correlation functions and Lyapunov spectra. An effective temperature is
attributed to the fluid-sliding state. Even though the velocity fluctuations
are Gaussian distributed, the fluid-sliding state is clearly not in equilibrium
because the equipartition theorem is violated. We also study the transition
between frozen states (stationary solutions) and=7F molten states
(fluid-sliding states). The transition is similar to a first-order phase
transition, and it shows hysteresis. The depinning-pinning transition
(freezing) is a nucleation process. The frozen state contains usually two
domains of different particle densities. The pinning-depinning transition
(melting) is caused by saddle-node bifurcations of the stationary states. It
depends on the history. Melting is accompanied by precursors, called
micro-slips, which reconfigurate the chain locally. Even though we investigate
the dynamics at zero temperature, the behavior of the Frenkel-Kontorova model
is qualitatively similar to the behavior of similar models at nonzero
temperature.Comment: Written in RevTeX, 13 figures in PostScript, appears in PR