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Thermal diffusion of sine-Gordon solitons

Niurka R. Quintero·Angel Sanchez·Franz G. Mertens
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Abstract

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 $\sqrt{t}$ 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.

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Niurka R. Quintero, Angel Sanchez, Franz G. Mertens. 2000-03-13. Thermal diffusion of sine-Gordon solitons. https://doi.org/10.1007/pl00011061

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