Low-temperature dynamics of sine-Gordon solitons

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Abstract
We examine the theory of a kink’s random walk in the classical sine-Gordon continuum at temperatures much lower than the kink’s rest energy. The description of the thermal bath in terms of phonons or breathers is shown to yield identical results for the diffusion constant, provided the underlying thermodynamic fluctuations are properly taken into account. We present molecular-dynamics evidence for the occurrence of the soliton-diffusion phenomenon and discuss the relevance of intrinsic discretization effects to numerical and experimental data.