  Motivated by recent experimental studies probing i) the existence of a mobile
layer at the free surface of glasses, and ii) the capillary leveling of polymer
nanofilms, we study the evolution of square-wave patterns at the free surface
of a generic glass-forming binary Lennard-Jones mixture over a wide temperature
range, by means of molecular dynamics simulations. The pattern's amplitude is
monitored and the associated decay rate is extracted. The evolution of the
latter as a function of temperature exhibits a crossover between two distinct
behaviours, over a temperature range typically bounded by the glass-transition
temperature and the mode-coupling critical temperature. Layer-resolved analysis
of the film particles' mean-squared displacements further shows that diffusion
at the surface is considerably faster than in the bulk, below the
glass-transition temperature. The diffusion coefficient of the surface
particles is larger than its bulk counterpart by a factor that reaches 105 at
the lowest temperature studied. This factor decreases upon heating, in
agreement with recent experimental studies.
