Localized-Mode Energy Losses in Large Excursions

During the motion of a defect in a crystal from one equilibrium position to an adjacent one, the associated localized mode (l.m.) undergoes large excursions, and large anharmonic forces are introduced. A new formulation for the resulting mode interaction is presented which appears more appropriate for this process than the usual expansion procedure. It is based on the introduction of curvilinear coordinates in configuration space. One coordinate line, ${\mathcal{C}}_1$, represents the motion of the system due to the large l.m. excursions, while the effect of the nonlocalized modes (n.l.m.) is to produce small oscillations orthogonal to ${\mathcal{C}}_1$. Anharmonic effects produce a finite curvature of ${\mathcal{C}}_1$ and it is shown that the rate of energy transfer from the l.m. to the n.l.m. is proportional to $R^{-2\mathrm{}}$, where $R$ is the radius of curvature of ${\mathcal{C}}_1$.