On the driven Frenkel-Kontorova model: I. Uniform sliding states and dynamical domains of different particle densities

Details On the driven Frenkel-Kontorova model: I. Uniform sliding states and dynamical domains of different particle densities On the driven Frenkel-Kontorova model: I. Uniform sliding states and dynamical domains of different particle densities

1998-05-22

arxiv.org/abs/cond-mat/9805287v1

Phys. Rev. E 58, p. 1601

Physics

Condensed Matter

Written in RevTeX, 9 figures in PostScript

Scientific paper

10.1103/PhysRevE.58.1601

The dynamical behavior of a harmonic chain in a spatially periodic potential (Frenkel-Kontorova model, discrete sine-Gordon equation) under the influence of an external force and a velocity proportional damping is investigated. We do this at zero temperature for long chains in a regime where inertia and damping as well as the nearest-neighbor interaction and the potential are of the same order. There are two types of regular sliding states: Uniform sliding states, which are periodic solutions where all particles perform the same motion shifted in time, and nonuniform sliding states, which are quasi-periodic solutions where the system forms patterns of domains of different uniform sliding states. We discuss the properties of this kind of pattern formation and derive equations of motion for the slowly varying average particle density and velocity. To observe these dynamical domains we suggest experiments with a discrete ring of at least fifty Josephson junctions.

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