Brownian Motion of a Kink in Sine-Gordon System and Diffusion Constant

Abstract

In a one-dimensional sine-Gordon system, a propagating vibration with small amplitude collides with a kink to produce a translation of the kink, giving rise to its Brownian-like motion, since incoming vibrations are excited thermally. The diffusion constant of the kink is obtained, at low temperatures, using the fluctuation-dissipation theorem and the thermal average over the vibrations. It turns out to be one eighth as large as that obtained previously by Fesser. This reduction would be due to the fact that wave packets of the incident vibrations overlap each other. Assuming the validity of the Einstein relation, we use the result to calculate the low field conductivity of quasi-one-dimensional substances at low temperatures. The magnitudes of the observed conductivity prefactors are reproduced for TaS₃, but not for TTF–TCNQ and TSeF–TCNQ.