Forces Between Kinks in ${\varphi }^8$ Theory

Abstract

We investigate the dynamics of the kinks that emerge in a one-dimensional scalar field theory with an octic potential containing a quartic minimum and two quadratic minima. We show analytically that kink-antikink and kink-kink pairs interact with a force that scales with the fourth power of the inter-kink distance, and calculate its strength. This is done using two different techniques. The first employs a collective coordinate method to approximately solve the equation of motion for the profile of an accelerating kink. The second is based on modifying the potential to one that is able to support static solutions containing multiple kinks. We show that the two methods give consistent results. All calculations are supported by numerical work that confirms the validity of our results.

21 pages, 13 figures

References in corpus (5)

• Kink-kink and kink-antikink interactions with long-range tails
• Long-range interactions of kinks
• Forces between Kinks and Antikinks with Long-range Tails
• Could the primordial radiation be responsible for vanishing of topological defects?
• Negative radiation pressure exerted on kinks

Cited by in corpus (11)

• Deformations of Kink Tails
• Kinks in higher-order polynomial models
• Super long-range kinks
• Highly-enhanced propagation of long-range kinks in heterogeneous media
• Exact BPS double-kinks in generalized ${\varphi }^4$, ${\varphi }^6$ and sine-Gordon models
• Long-range interaction of kinks in higher-order polynomial models
• Domain wall thickness and deformations of the field model
• Analytical short- and long-range kink-like structures in scalar field models with polynomial interactions
• From thin to thick domain walls: An example of the ${\phi }^8$ model
• Vibrations of thick domain walls: How to avoid no-go theorem
• Kink dynamics in a high-order field model