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

TL;DR

This paper derives a generalized Langevin equation describing the motion of an ad-atom on a substrate influenced by a standing acoustic wave, providing a theoretical framework for understanding wave-induced diffusion effects.

Contribution

It presents an analytical derivation of the ad-atom's motion equation from the full Hamiltonian, highlighting the effective force's dependence on the acoustic wave.

Findings

The derived equation captures the wave's influence on ad-atom dynamics.

The effective force mirrors the spatial and temporal patterns of the standing wave.

A detailed analysis of the terms in the Langevin equation is provided.

Abstract

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.