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

doi:https://doi.org/10.1103/PhysRevLett.122.171601

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 φ ²ⁿ⁺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 (φ ⁸ model), n = 3 (φ ¹⁰ model), and n = 4 (φ ¹² model).

Authors:: Christov, Ivan C.; Decker, Robert J.; Demirkaya, A.; Gani, Vakhid A.; Kevrekidis, P. G.; Khare, Avinash; Saxena, Avadh

Publication Date:: 2019-05-03

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:: Journal Article: 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.

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                    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.  https://doi.org/10.1103/PhysRevLett.122.171601

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                    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.  https://doi.org/10.1103/PhysRevLett.122.171601.

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@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},

  url          = {https://www.osti.gov/biblio/1510543},
  journal      = {Physical Review Letters},

  issn         = {0031-9007},

  number       = 17,

  volume       = 122,

  place        = {United States},

  year         = {2019},

  month        = {5}

}

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Cited by: 9 works

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Figures / Tables:

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 φ ⁸ model. The dashed lines are computed numerically, and the solid lines are computed analytically. Top right is themore »

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Multi-kink scattering in the double sine-Gordon model
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Similar Records

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

Abstract

Citation Formats

Figures / Tables:

From supersymmetric quantum mechanics to scalar field theories journal, April 2017

Collective coordinates in one-dimensional soliton models revisited journal, October 2016

Kink excitation spectra in the (1+1)-dimensional φ8 model journal, August 2015

Forces between kinks and antikinks with long-range tails journal, January 2019

Kink-Antikink Collisions in the ϕ 6 Model journal, August 2011

Long-range interactions of kinks journal, January 2019

A scattering theory of ultrarelativistic solitons journal, November 2013

Successive phase transitions and kink solutions in ϕ 8 , ϕ 10 , and ϕ 12 field theories journal, August 2014

Clash of Kinks: Phase Shifts in Colliding Nonintegrable Solitons journal, November 2013

Creating Kinks from Particles journal, September 2008

Crystallization of proteins accompanied by formation of a cylindrical surface journal, September 1997

Kink interactions in the ( 1 + 1 ) -dimensional φ 6 model journal, June 2014

Topological defects with long-range interactions journal, July 1998

Soliton structures in P ( φ ) 2 journal, December 1979

Resonance structure in kink-antikink interactions in φ4 theory journal, October 1983

Analytical study of kinklike structures with polynomial tails journal, May 2018

Kink dynamics in a parametric ϕ6 system: a model with controllably many internal modes journal, December 2017

Motion of Domain Walls and the Dynamics of Kinks in the Magnetic Peierls Potential journal, November 2014

New scalar field models and their defect solutions journal, February 2011

Deformed defects for scalar fields with polynomial interactions journal, May 2006

On the ferroelastic phase transition of LiNH 4 SO 4 : a Brillouin scattering study and theoretical modelling journal, January 1989

Multi-kink collisions in the ϕ 6 model journal, July 2017

Highly interactive kink solutions journal, July 2012

Scattering of the φ8 kinks with power-law asymptotics journal, February 2019

Solitons in condensed matter: A paradigm journal, April 1980

Kink Collisions in Curved Field Space journal, April 2015

Multi-kink scattering in the double sine-Gordon model journal, July 2019

Multi-kink scattering in the double sine-Gordon model journal, July 2019

Solvable self-dual impurity models journal, July 2019

Family of potentials with power law kink tails journal, August 2019

Kink scattering in hyperbolic models journal, November 2019

From supersymmetric quantum mechanics to scalar field theories
journal, April 2017

Collective coordinates in one-dimensional soliton models revisited
journal, October 2016

Kink excitation spectra in the (1+1)-dimensional φ8 model
journal, August 2015

Forces between kinks and antikinks with long-range tails
journal, January 2019

Kink-Antikink Collisions in the $ϕ^{6}$ Model
journal, August 2011

Long-range interactions of kinks
journal, January 2019

A scattering theory of ultrarelativistic solitons
journal, November 2013

Successive phase transitions and kink solutions in $ϕ^{8}$ , $ϕ^{10}$ , and $ϕ^{12}$ field theories
journal, August 2014

Clash of Kinks: Phase Shifts in Colliding Nonintegrable Solitons
journal, November 2013

Creating Kinks from Particles
journal, September 2008

Crystallization of proteins accompanied by formation of a cylindrical surface
journal, September 1997

Kink interactions in the $(1 + 1)$ -dimensional $φ^{6}$ model
journal, June 2014

Topological defects with long-range interactions
journal, July 1998

Soliton structures in $P {(φ)}_{2}$
journal, December 1979

Resonance structure in kink-antikink interactions in φ4 theory
journal, October 1983

Analytical study of kinklike structures with polynomial tails
journal, May 2018

Kink dynamics in a parametric ϕ6 system: a model with controllably many internal modes
journal, December 2017

Motion of Domain Walls and the Dynamics of Kinks in the Magnetic Peierls Potential
journal, November 2014

New scalar field models and their defect solutions
journal, February 2011

Deformed defects for scalar fields with polynomial interactions
journal, May 2006

On the ferroelastic phase transition of LiNH ₄ SO ₄ : a Brillouin scattering study and theoretical modelling
journal, January 1989

Multi-kink collisions in the ϕ 6 model
journal, July 2017

Highly interactive kink solutions
journal, July 2012

Scattering of the φ8 kinks with power-law asymptotics
journal, February 2019

Solitons in condensed matter: A paradigm
journal, April 1980

Kink Collisions in Curved Field Space
journal, April 2015

Multi-kink scattering in the double sine-Gordon model
journal, July 2019

Multi-kink scattering in the double sine-Gordon model
journal, July 2019

Solvable self-dual impurity models
journal, July 2019

Family of potentials with power law kink tails
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Kink scattering in hyperbolic models
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