Discrete theory of kink diffusion in theφ4lattice with comparison to the continuum approximation

We use the memory function formalism to study kink dynamics in a thermal ${\phi }^4$ lattice. By introducing kink-fluctuation interactions as a perturbation, and by including discrete effects of kink structure nonperturbatively, we are able to reproduce the qualitative behavior of the kink diffusion constant $D_K$ and the kink-velocity autocorrelation spectrum as calculated from molecular-dynamics simulation. The continuum approximation obtained by ignoring discrete structure associated with the lattice kink yields results which are qualitatively incorrect at low temperatures and weak inter- atomic coupling. In particular, $D_K$ goes to zero at low temperatures only when the discrete structure of the kink is included.