Kink dynamics in a one-dimensional double-well field theory

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Abstract
We have studied the dynamics of kinks in a one-dimensional model field theory. We have extended the method we developed earlier for treating multikink configurations for studying the equilibrium properties to the time-dependent case. We have calculated the dynamic structure factor for the displacement fields. We obtain a sharp central peak (a Lorentzian about zero frequency) for small wave numbers and low temperatures. As we increase the wave number or temperature, the central peak broadens and loses weight. We also find a phonon peak at low temperatures which is highly damped and softened for very small wave numbers, but it sharpens for larger wave numbers. We have also evaluated the kink velocity autocorrelation function which has an oscillatory component due to the interaction of the kinks with the phonons. As expected, the mean free path of the kinks becomes very long as the temperature of the system is reduced.