Viscosity of a Kink in the One-Dimensional φ4System

Viscosity of a kink in the one-dimensional φ 4 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 B T ) 2 are performed to find that the static limit of the viscosity is \((ω=0)=0.1224{1}{φ₀⁴}({kBT}{mldω₀²})²ω₀+O(kBT)³\), where φ 0 is a displacement at which the φ 4 local potential is minimum, m mass of an ion, l lattice constant, d width of the kink and ω 0 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 B T ) 2 .