Unidimensional model of the ad-atom diffusion on a substrate submitted to a standing acoustic wave I. Derivation of the ad-atom motion equation

The effect of a standing acoustic wave on the diffusion of an ad-atom on a cryst alline surface is theoretically studied. We used an unidimensional space model to study the ad-atom+substrate system. The dynamic equation of the ad-atom, a Generalized Langevin equation, is analyti cally derived from the full Hamiltonian of the ad-atom+substrate system submitt ed to the acoustic wave. A detailed analysis of each term of this equation, as well as of their propertie s, is presented. Special attention is devoted to the expression of the effective force induced by the wave on the ad-atom. It has essentially the same spatial and time dependenc es as its parent standing acoustic wave.