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.

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

References in corpus (2)

• Kink-kink and kink-antikink interactions with long-range tails
• Long-range interactions of kinks

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