Viscosity of a Kink in the One-Dimensional φ⁴ System

Abstract

Viscosity of a kink in the one-dimensional φ⁴ system is investigated. It is generated by momentum transfer between the kink and phonons. Mori’s formula for the viscosity is calculated in a form of low temperature expansion, using the collective coordinate method, in which the kink location is defined as a dynamical variable. Calculations up to the order of (k_BT)² are performed to find that the static limit of the viscosity is
(Remark: Graphics omitted.),
where φ₀ is a displacement at which the φ⁴ local potential is minimum, m mass of an ion, l lattice constant, d width of the kink and ω₀ characteristic frequency of the phonons. Relation between the viscosity and diffusion constant is discussed and two mechanisms are pointed out for Brownian-like motion of the kink. In the sine-Gordon system, the viscosity of the soliton is shown to be zero up to the order of (k_BT)².