Dynamics of non-linear systems: The kink-phonon interaction

The interaction between non-linear elementary excitations (kinks) and phonons is examined, within the context of perturbation theory previously developed by Hasenfratz and Klein, for the case of the ⁴-model. It is demonstrated that the effect of a kink-phonon collision will be a shift in the kink's position, for which an analytical expression is given. It is conjectured that, as thermal phonons collide with the kink, the latter performs a purely diffusive motion. An estimate of the kink diffusion constant is given, based on a simple kinetic theory of kink-phonon collisions. The light scattering spectrum of a gas of non-interacting moving kinks with a thermal velocity distribution function is calculated; a central peak is found, whose structure reflects the kinks' diffusion.