Self-Diffusion via Sine-Gordon Solitons

Theoretical evidence is presented that for temperatures so low that kBT 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 t1/2 for times much longer than microscopic times but much shorter than the soliton lifetime τ. For times much greater than τ, linear behavior is suggested. Finite-size effects are discussed in the context of recent computer simulation studies.