Forces between Kinks and Antikinks with Long-range Tails

TL;DR

This paper investigates the forces between kinks and antikinks with long-range tails in a scalar field theory, revealing that kink-kink interactions are repulsive and four times stronger than kink-antikink attractions, with forces decaying as the fourth power of separation.

Contribution

It introduces a nonlinear method using an adiabatic ansatz to calculate forces between long-range tail kinks, providing new quantitative insights.

Findings

Kink-kink force is repulsive and decays as 1/r^4.

Kink-antikink force is attractive and decays as 1/r^4.

Kink-kink repulsion is four times stronger than kink-antikink attraction.

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.