Linear Response of One Dimensional Nonlinear System. I. Dynamical Properties of the φ⁴ Chain

Abstract

The linear response theory of the one dimensional nonlinear systems is formulated in the limit of the overdamping. Transfer integral method is applied to investigate the dynamical structure factor S(k=0, ω). The equation of motion for the distribution function is reduced to a set of independent equations for normal modes. As an example the structure factor for the φ⁴ chain is calculated to be the sum of a very narrow central peak and a broad overdamped phonon peak. The origin of the former is supposed to be the domain wall motion.