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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.
We present a modified version of the one-dimensional sine-Gordon that exhibits a thermodynamic, roughening phase transition, in analogy with the 2D usual sine-Gordon model. The model is suited to study the crystalline growth over an impenetrable subs
We study whether or not sine-Gordon kinks exhibit internal modes or ``quasimodes. By considering the response of the kinks to ac forces and initial distortions, we show that neither intrinsic internal modes nor ``quasimodes exist in contrast to previ
Motivated by the recently developed duality between elasticity of a crystal and a symmetric tensor gauge theory by Pretko and Radzihovsky, we explore its classical analog, that is a dual theory of the dislocation-mediated melting of a two-dimensional
Nonlinear space-time dynamics, defined in terms of celebrated solitonic equations, brings indispensable tools for understanding, prediction and control of complex behaviors in both physical and life sciences. In this paper, we review sine-Gordon soli
In this reply to the comment by C. R. Willis, we show, by quoting his own statements, that the simulations reported in his original work with Boesch [Phys. Rev. B 42, 2290 (1990)] were done for kinks with nonzero initial velocity, in contrast to what