Forces between Kinks and Antikinks with Long-range Tails
Abstract
In a scalar field theory with a symmetric octic potential having a quartic minimum and two quadratic minima, kink solutions have long-range tails. We calculate the force between two kinks and between a kink and an antikink when their long-range tails overlap. This is a nonlinear problem, solved using an adiabatic ansatz for the accelerating kinks that leads to a modified, first-order Bogomolny equation. We find that the kink-kink force is repulsive and decays with the fourth power of the kink separation. The kink-antikink force is attractive and decays similarly. Remarkably, the kink-kink repulsion has four times the strength of the kink-antikink attraction.
Cite
@article{arxiv.1810.03557,
title = {Forces between Kinks and Antikinks with Long-range Tails},
author = {N. S. Manton},
journal= {arXiv preprint arXiv:1810.03557},
year = {2019}
}
Comments
23 pages, 3 figures. Revised version with new figures. Incorporates arXiv preprint 1810.00788, and compares Kink-Kink and Kink-Antikink forces. Accepted Manuscript version accepted for publication in J. Phys. A: Mathematical and Theoretical