  We extend the study of velocity quantization phenomena recently found in the
classical motion of an idealized 1D model solid lubricant -- consisting of a
harmonic chain interposed between two periodic sliding potentials [Phys. Rev.
Lett. 97, 056101 (2006)]. This quantization is due to one slider rigidly
dragging the commensurate lattice of kinks that the chain forms with the other
slider. In this follow-up work we consider finite-size chains rather than
infinite chains. The finite size (i) permits the development of robust velocity
plateaus as a function of the lubricant stiffness, and (ii) allows an overall
chain-length re-adjustment which spontaneously promotes single-particle
periodic oscillations. These periodic oscillations replace the quasi-periodic
motion produced by general incommensurate periods of the sliders and the
lubricant in the infinite-size model. Possible consequences of these results
for some real systems are discussed.
