Linear Response of One Dimensional Nonlinear System. II

The linear response theory of the one dimensional nonlinear system, developed in I, is generalized to apply to a system with an arbitrary damping strength. In stead of the Smoluchowsky equation, the Fokker Planck equation is investigated. The transfer integral method is again applicable with a simple decoupling approximation. The dynamical structure factor for the φ⁴chain is found to be the sum of phonon peaks and a sharp central peak. As the damping strength reduces, the phonon peak becomes underdamped, while the structure of the cetatral peak is essentially the same as the strong damping case. The origin of the central peak is due to the response of the domain wall.