Resonance-induced cluster-mobility: Dynamics of a finite Frenkel-Kontorova model

Statics and dynamics of a finite incommensurate Frenkel-Kontorova chain are studied in the framework of both continuum and discrete models. Since the ground state of the finite chain is not degenerate it cannot freely slide along the substrate, i.e., the finite chain does not possess the “supermobility” of the infinitely long incommensurate chain. Instead, the finite chain shows a “resonance mobility”. Simulating the behaviour of the finite chain in an external field we observe resonances around the lowest frequency in the acoustic branch of the chain spectrum. This frequency depends on the chain size and the degree of incommensurability and corresponds to vibration “in-phase” of all solitons in the chain. The resonance leads to a significantly increased diffusive mobility of clusters of a specific size. This selectively enhanced cluster-mobility persists also in the presence of stochastic forces and friction.