Stochastic dynamics of a subsystem interacting with a solid body with application to diffusive processes in solids

Abstract

In this paper the dynamics of a mechanical subsystem interacting with a solid body is studied. The Newton equations are transformed to a set of stochastic generalized Langevin equations describing the evolution of the coordinates of the subsystem particles. The solid is modeled as a bath of interacting harmonic oscillators, and the effect of their spatial correlations on the statistical properties of the Langevin forces is accounted for. The most important result is the relation established between the static interaction of the subsystem with the solid body and the dissipative and fluctuation forces. In the particular case of a subsystem consisting of a single particle, an expression is derived for the friction tensor in terms of the static interaction potential and Debye cutoff frequency of the solid. The analysis is applied in the latter case to some simple processes occurring in solids, such as adsorption, desorption, and diffusion.