Molecular dynamics study of lattice kink diffusion

Single-kink diffusion is simulated in a ${\phi }^4$ lattice by the method of molecular dynamics. The temperature dependence of the single-kink diffusion constant $D_K$ is obtained from the kink meansquare displacement and velocity autocorrelation function. When system parameters are chosen such that discrete lattice effects are significant, kink diffusion is found to be a random-walk process that requires thermal activation of the kink over its Peierls barrier. Short-time behavior of the kink velocity autocorrelation function reveals trapped oscillations and damped propagation of the kink.