  The effect of a standing acoustic wave on the diffusion of an ad-atom on a
crystalline 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 analytically derived from the full
Hamiltonian of the ad-atom+substrate system submitted to the acoustic wave. A
detailed analysis of each term of this equation, as well as of their
properties, 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 dependences as its parent standing acoustic wave.
