Effective kink-kink interaction in a one-dimensional model mediated by phonon exchange

Abstract

The general 1D double-well model with anharmonic interaction is considered in the displacive limit.Expansion of the Hamiltonian around a multikink state results in a phonon-kink Hamiltonian. lt is shown that at rather low temperatures and short wavelengths the phonon-kink interaction can be treated in Born approximation, leading to a decomposition of the multikink-phonon Hamiltonian. Elimination of the phonons results in an eA'ective potential for the kink-kink interaction, which corresponds to the one-dimensional analog of the RKKY interaction. This long-range interaction is inherent only for models with anharmonic on-site potentials and not in case of a double-parabola model.

Solitary waves with friction in one-dimensional anisotropic magnets

“…Wada and co-workers [11] examined the nonlinear interaction between solitary excitations and linear oscillating modes of the sine-Gordon equation, and, as a result of the coupling, they found diffusive motion of the former. Quite 0953-8984/96/224031+14$19.50 c 1996 IOP Publishing Ltd similarly, Rostiashvili and Schilling [12] showed that the coupling of domain walls to spatial fluctuations of the magnetization leads to an effective kink-kink interaction. Here we investigate the coupling of the sine-Gordon field to the surrounding lattice vibrations.…”