Momentum Transfer between a Kink and a Phonon in the One-Dimensional φ⁴ System

Abstract

Higher order collision process between a kink and a phonon is investigated in the one-dimensional φ⁴ system. Diagrammatic perturbation method is used, where the amplitude of the phonon is the smallness parameter. It is shown that the phonon transfers the momentum to the kink in the fourth order. The momentum transfer is obtained by the contributions of poles of order two in the integrals over momenta. The final velocity of the kink, derived as a function of the incident phonon wave number, reproduces exactly the result of the previous discussion using conservation laws. The kink, which is not moving at first, begins to move after the collision in the direction of the incident phonon. The effective interaction between them is attractive. Possible mechanisms which determine the viscosity of the kink are pointed out.