Thermal diffusion of sine-Gordon solitons

We analyze the diffusive motion of kink solitons governed by the thermal sine-Gordon equation. We analytically calculate the correlation function of the position of the kink center as well as the diffusion coefficient, both up to second-order in temperature. We find that the kink behavior is very similar to that obtained in the overdamped limit: There is a quadratic dependence on temperature in the diffusion coefficient that comes from the interaction among the kink and phonons, and the average value of the wave function increases with √ t due to the variance of the centers of individual realizations and not due to kink distortions. These analytical results are fully confirmed by numerical simulations. PACS. 05.40.-a Fluctuation phenomena, random processes, noise and Brownian motion – 05.45.-a Nonlinear dynamics and nonlinear dynamical systems – 74.50.+r Proximity effects, weak links, tunneling phenomena, and Josephson effects – 85.25.Cp Josephson devices