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Title: Kink-Kink and Kink-Antikink Interactions with Long-Range Tails

Abstract

In this Letter, we address the long-range interaction between kinks and antikinks, as well as kinks and kinks, in φ2n+4 field theories for n > 1. The kink-antikink interaction is generically attractive, while the kink-kink interaction is generically repulsive. We find that the force of interaction decays with the 2n/(n–1)th power of their separation, and we identify the general prefactor for arbitrary n. Importantly, we test the resulting mathematical prediction with detailed numerical simulations of the dynamic field equation, and obtain good agreement between theory and numerics for the cases of n = 2 (φ8 model), n = 3 (φ10 model), and n = 4 (φ12 model).

Authors:
; ; ; ; ; ;
Publication Date:
Research Org.:
Los Alamos National Lab. (LANL), Los Alamos, NM (United States)
Sponsoring Org.:
USDOE Laboratory Directed Research and Development (LDRD) Program
OSTI Identifier:
1510543
Alternate Identifier(s):
OSTI ID: 1532709
Report Number(s):
LA-UR-18-30946
Journal ID: ISSN 0031-9007; PRLTAO; 171601
Grant/Contract Number:  
02.a03.21.0005; 89233218CNA000001
Resource Type:
Published Article
Journal Name:
Physical Review Letters
Additional Journal Information:
Journal Name: Physical Review Letters Journal Volume: 122 Journal Issue: 17; Journal ID: ISSN 0031-9007
Publisher:
American Physical Society
Country of Publication:
United States
Language:
English
Subject:
72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS; 71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSICS; Mathematics

Citation Formats

Christov, Ivan C., Decker, Robert J., Demirkaya, A., Gani, Vakhid A., Kevrekidis, P. G., Khare, Avinash, and Saxena, Avadh. Kink-Kink and Kink-Antikink Interactions with Long-Range Tails. United States: N. p., 2019. Web. doi:10.1103/PhysRevLett.122.171601.
Christov, Ivan C., Decker, Robert J., Demirkaya, A., Gani, Vakhid A., Kevrekidis, P. G., Khare, Avinash, & Saxena, Avadh. Kink-Kink and Kink-Antikink Interactions with Long-Range Tails. United States. doi:10.1103/PhysRevLett.122.171601.
Christov, Ivan C., Decker, Robert J., Demirkaya, A., Gani, Vakhid A., Kevrekidis, P. G., Khare, Avinash, and Saxena, Avadh. Fri . "Kink-Kink and Kink-Antikink Interactions with Long-Range Tails". United States. doi:10.1103/PhysRevLett.122.171601.
@article{osti_1510543,
title = {Kink-Kink and Kink-Antikink Interactions with Long-Range Tails},
author = {Christov, Ivan C. and Decker, Robert J. and Demirkaya, A. and Gani, Vakhid A. and Kevrekidis, P. G. and Khare, Avinash and Saxena, Avadh},
abstractNote = {In this Letter, we address the long-range interaction between kinks and antikinks, as well as kinks and kinks, in φ2n+4 field theories for n > 1. The kink-antikink interaction is generically attractive, while the kink-kink interaction is generically repulsive. We find that the force of interaction decays with the 2n/(n–1)th power of their separation, and we identify the general prefactor for arbitrary n. Importantly, we test the resulting mathematical prediction with detailed numerical simulations of the dynamic field equation, and obtain good agreement between theory and numerics for the cases of n = 2 (φ8 model), n = 3 (φ10 model), and n = 4 (φ12 model).},
doi = {10.1103/PhysRevLett.122.171601},
journal = {Physical Review Letters},
number = 17,
volume = 122,
place = {United States},
year = {2019},
month = {5}
}

Journal Article:
Free Publicly Available Full Text
Publisher's Version of Record
DOI: 10.1103/PhysRevLett.122.171601

Citation Metrics:
Cited by: 9 works
Citation information provided by
Web of Science

Figures / Tables:

FIG. 1 FIG. 1: Top left is the log-log plot of the left kink acceleration a as a function of A for the kink-kink interaction (blue) and kinkantikink interaction (red) in the φ8 model. The dashed lines are computed numerically, and the solid lines are computed analytically. Top right is the plotmore » of the initializers for the kink-kink (K-K) (blue-solid) and kink-antikink (K-AK) (red-dashed) interaction. Bottom left is the space-time contour plot of the K-AK interaction, and the cyan curve with circle symbols is the plot of the solution to the initial value problem (IVP): ẍ(t) = −11.0785=x4, x(0) = 20, ẋ(0) = 0. Bottom right is the spacetime contour plot of the K-K interaction, and the cyan curve with circle symbols is the solution to the IVP: ẍ(t) = 44.3139=x4, x(0) = 20, ẋ(0) = 0.« less

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