https://doi.org/10.1007/PL00011061
Thermal diffusion of sine-Gordon solitons
1
Grupo Interdisciplinar de Sistemas
Complicados (GISC), Departamento de Matemáticas,
Universidad Carlos III de Madrid,
Edificio Sabatini,
Avenida de la Universidad 30,
28911 Leganés, Madrid, Spain
2
Physikalisches Institut, Universität Bayreuth,
95440 Bayreuth, Germany
Received:
4
October
1999
Revised:
3
February
2000
Published online: 15 July 2000
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
© EDP Sciences, Società Italiana di Fisica, Springer-Verlag, 2000
