Solitons and exact velocity quantization of incommensurate sliders

We analyse in some detail the recently discovered velocity quantization phenomena in the classical motion of an idealized one-dimensional solid lubricant, consisting of a harmonic chain interposed between two periodic sliders. The ratio w = upsilon(cm)/upsilon(ext) of the chain centre-of-mass velocity to the externally imposed relative velocity of the sliders is pinned to exact 'plateau' values for wide ranges of parameters, such as sliders corrugation amplitudes, external velocity, chain stiffness and dissipation, and is strictly determined by the commensurability ratios alone. The phenomenon is caused by one slider rigidly dragging the density solitons (kinks/antikinks) that the chain forms with the other slider. Possible consequences of these results for some real systems are discussed.