Nonlinear Dynamics of Interstitial Atom

where m is the mass of the particle and γ is the friction constant, (t) is the random force with zero mean and a nonzero variance. As an example let us mention a generalized Langevin equation describing dynamics of atoms interacting with thermal vibrations of the crystal lattice derived in Ref. [2]. Both the friction and the random force are very crude phenomenological substitutes of the real coupling of the particle to a heat bath. We hope that in á lattice system one can formulate a Fokker—Planck equation which describes diffusive motion and is free of that shortcoming. The first step is done in the present paper. It consists in derivation of the equation of motion in periodic potential for interstitial atom driven by phonons of wave vector q and frequency ω(q). In recent years, following the paper of Chirikov [3], studies on diffusion in deterministic systems get increasing interest. The deterministic diffusion is thought to be an interesting manifestation of classical chaos. In the present paper we consider a particular case of deterministic equation related to diffusion of an impurity atom. Many important processes occurring in solids are the result of interaction of the lattice vibrations with other subsystems. The one we are interested in is the phonons driven transport of interstitial atom