Forces Between Kinks in \(\phi^8\) Theory

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 inte...

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Bibliographic Details
Published inarXiv.org
Main Author Peru d'Ornellas
Format Paper
LanguageEnglish
Published Ithaca Cornell University Library, arXiv.org 17.06.2020
Subjects
Equations of motion
Field theory
Scalars
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Summary: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.
ISSN:2331-8422
DOI:10.48550/arxiv.2001.10744