Single-kink dynamics in a one-dimensional atomic chain: A nonlinear atomistic theory and numerical simulation

A nonlinear lattice-dynamical theory of single kinks is presented which involves a simple equation of constraint. A set of coupled equations of motion is derived for the kink and discrete lattice fluctuations, which retains the full details of their mutual interaction. The theory is used to study ${\ensuremath{\varphi}}^{4}$-lattice kinks. For low kink velocities the kink equation of motion reduces to a generalized Langevin form. The static kink energy is found to vary periodically with the lattice spacing, implying that thermal kink motion is an activation process at low temperatures. Numerical studies reveal that kinks undergo damped motion, oscillatory motion, and trapping between lattice sites. Damping and oscillatory motion vanish as the continuum limit is approached. A phenomenological theory of damped kink propagation is developed and compared with numerical simulation.