Kink plateau dynamics in finite-size lubricant chains

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.