  In the framework of Langevin dynamics, we demonstrate clear evidence of the
peculiar quantized sliding state, previously found in a simple 1D boundary
lubricated model [Phys. Rev. Lett. 97, 056101 (2006)], for a substantially less
idealized 2D description of a confined multi-layer solid lubricant under shear.
This dynamical state, marked by a nontrivial ``quantized'' ratio of the
averaged lubricant center-of-mass velocity to the externally imposed sliding
speed, is recovered, and shown to be robust against the effects of thermal
fluctuations, quenched disorder in the confining substrates, and over a wide
range of loading forces. The lubricant softness, setting the width of the
propagating solitonic structures, is found to play a major role in promoting
in-registry commensurate regions beneficial to this quantized sliding. By
evaluating the force instantaneously exerted on the top plate, we find that
this quantized sliding represents a dynamical ``pinned'' state, characterized
by significantly low values of the kinetic friction. While the quantized
sliding occurs due to solitons being driven gently, the transition to ordinary
unpinned sliding regimes can involve lubricant melting due to large
shear-induced Joule heating, for example at large speed.

Materials Science