The power law time dependence of ( R2) in non-equilibrium growth

Abstract. Model systems evolving in time to atfain equilibrium, with spin exchange dynamics, order by forming domains &er a [emperawe quench within the ordered region They are described in terms of time-dependent diffusion coefficientr and a distribution of activation energies. This description is analogous to the relaxation in disordered systems such as a:Si-H (amorphous hydrogenated Si). Diffusive motion in solids [I], described usually in terms of a particle executing a random walk in a periodic potential, is characterized by the mean square displacement, (R’) , that grows linearly with time. The temperature dependence of the diffusion coefficient has an activated form, with the activation energy the depth of the potential well. For systems with a finite number of particles and no interactions (except site exclusion where two particles cannot occupy the same site simultaneously), ( R z) still grows linearly with time. The diffusion coefficient has the same activation energy but the prefactor is modified by the so-called lattice correlation factor, which expresses the tendency of a particle to jump into the hole left behind by a neighbouring particle that has already jumped. It only depends on the lattice geometry and the number of particles present. In this case, the mean squar