To understand the tribological properties of Ne and Kr on Pb(111), the potential energy surfaces for sliding motion of Ne, Kr, and Xe monolayers on the Pb(111) surface are examined through density functional calculations, using either local density or self-consistent nonlocal van der Waals functionals. The calculated adsorption energy for Xe/Pb(111) agrees well with experiment, validating the present approach and parameters. Activation energies along a sliding path indicate that Ne motion is much faster than Kr and Xe on Pb(111) at T∼6  K, which explains the puzzling experimental observation.

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We consider the underdamped dynamics of a chain of atoms subject to a dc driving force and a quasiperiodic substrate potential. The system has three inherent length scales which we take to be mutually incommensurate. We find that when the length scales are related by the spiral mean (a cubic irrational) there exists a value of the interparticle interaction strength above which the static friction is zero. When the length scales are related by the golden mean (a quadratic irrational) the static friction is always nonzero. From considerations based on the connection of this problem to standard map theory, we postulate that zero static friction is generally possible for incommensurate ratios of the length scales involved. However, when the length scales are quadratic irrationals, or have some commensurability with each other, the static friction will be nonzero for all choices of interaction parameters. We also comment on the nature of the depinning mechanisms and the steady states achieved by the moving chain.