Incommensurability of a confined system under shear

We study a chain of harmonically interacting atoms confined between two sinusoidal substrate potentials, when the top substrate is driven through an attached spring with a constant velocity. This system is characterized by three inherent length scales and closely related to physical situations with confined lubricant films. We show that, contrary to the standard Frenkel-Kontorova model, the most favorable sliding regime is achieved by choosing chain-substrate incommensurabilities belonging to the class of cubic irrational numbers (e.g., the spiral mean). At large chain stiffness, the well known golden mean incommensurability reveals a very regular time-periodic dynamics with always higher kinetic friction values with respect to the spiral mean case.