Justification for the use of Markovian Langevin statistics in the modelling of activated surface diffusion

Low temperature surface diffusion is driven by the thermally activated hopping of adatoms between adsorption sites. Helium spin-echo techniques, capable of measuring the sub-picosecond motion of individual adatoms, have enabled the bench-marking of many important adsorbate-substrate properties. The well-known Markovian Langevin equation has emerged as the standard tool for the interpretation of such experimental data, replacing adatom-substrate interactions with stochastic white noise and linear friction. However, the consequences of ignoring the colored noise spectrum and non-linearities inherent to surface systems are not known. Through the computational study of three alternative models of adatom motion, we show that the hopping rate and jump distributions of an adatom are fixed to within a few percent by the potential energy surface and a new generalized energy exchange rate parameter alone, independent of the model used. This result justifies the use of the Markovian Langevin equation, regardless of the true statistical nature of adatom forces, provided results are quoted in terms of the new energy exchange rate parameter. Moreover, numerous mechanisms for the effect of noise correlations and non-linear friction on the energy exchange rate are proposed which likely contribute to activated surface diffusion and activated processes more generally.