Quasielastic He atom scattering from surfaces: A stochastic description of the dynamics of interacting adsorbates

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.