Self-Diffusion via Sine-Gordon Solitons

Theoretical evidence is presented that for temperatures so low that $k_{\mathrm{B}}T$ is much less than the rest energy of a soliton, the mean square displacement of a diffusing particle of an infinite sine-Gordon chain behaves as $t^{\frac{1}{2}}$ for times much longer than microscopic times but much shorter than the soliton lifetime $\tau$. For times much greater than $\tau$, linear behavior is suggested. Finite-size effects are discussed in the context of recent computer simulation studies.