  The study of diffusion and low frequency vibrational motions of particles on
metal surfaces is of paramount importance; it provides valuable information on
the nature of the adsorbate-substrate and the substrate-substrate interactions.
In particular, the experimental broadening observed in the diffusive peak with
increasing coverage is usually interpreted in terms of a dipole-dipole like
interaction among adsorbates via extensive molecular dynamics calculations
within the Langevin framework. Here we present an alternative way to interpret
this broadening by means of a purely stochastic description, namely the
interacting single adsorbate approximation, where two noise sources are
considered: (1) a Gaussian white noise accounting for the surface friction and
temperature, and (2) a white shot noise replacing the interaction potential
between adsorbates. Standard Langevin numerical simulations for flat and
corrugated surfaces (with a separable potential) illustrate the dynamics of Na
atoms on a Cu(100) surface which fit fairly well to the analytical expressions
issued from simple models (free particle and anharmonic oscillator) when the
Gaussian approximation is assumed. A similar broadening is also expected for
the frustrated translational mode peaks.
