Kink dynamics in a parametric Φ6 system: a model with controllably many internal modes

Demirkaya, A.; Decker, R.; Kevrekidis, P. G.; Christov, I. C.; Saxena, Avadh

doi:10.1007/JHEP12(2017)071

Title: Kink dynamics in a parametric Φ⁶ system: a model with controllably many internal modes

Abstract

We explore a variant of the Φ⁶ model originally proposed in Phys. Rev.D 12 (1975) 1606 as a prototypical, so-called, “bag” model in which domain walls play the role of quarks within hadrons. We examine the steady state of the model, namely an apparent bound state of two kink structures. We explore its linearization, and we find that, as a function of a parameter controlling the curvature of the potential, an effectively arbitrary number of internal modes may arise in the point spectrum of the linearization about the domain wall profile. We explore some of the key characteristics of kink-antikink collisions, such as the critical velocity and the multi-bounce windows, and how they depend on the principal parameter of the model. We find that the critical velocity exhibits a non-monotonic dependence on the parameter controlling the curvature of the potential. For the multi-bounce windows, we find that their range and complexity decrease as the relevant parameter decreases (and as the number of internal modes in the model increases). We use a modified collective coordinates method [in the spirit of recent works such as Phys. Rev.D 94 (2016) 085008] in order to capture the relevant phenomenology in a semi-analytical manner.

Authors:

Demirkaya, A. ^[1]; Decker, R. ^[1]; Kevrekidis, P. G. ^[2]; Christov, I. C. ^[3];

^[4]

University of Hartford, West Hartford, CT (United States)
Univ. of Massachusetts, Amherst, MA (United States)
Los Alamos National Lab. (LANL), Los Alamos, NM (United States); Purdue Univ., West Lafayette, IN (United States)
Los Alamos National Lab. (LANL), Los Alamos, NM (United States)

Publication Date:: 2017-12-14

Research Org.:: Los Alamos National Lab. (LANL), Los Alamos, NM (United States)

Sponsoring Org.:: USDOE National Nuclear Security Administration (NNSA); USDOE Laboratory Directed Research and Development (LDRD) Program

OSTI Identifier:: 1415382

Report Number(s):: LA-UR-17-24150
Journal ID: ISSN 1029-8479; TRN: US1800784

Grant/Contract Number:: AC52-06NA25396

Resource Type:: Accepted Manuscript

Journal Name:: Journal of High Energy Physics (Online)

Additional Journal Information:: Journal Name: Journal of High Energy Physics (Online); Journal Volume: 2017; Journal Issue: 12; Journal ID: ISSN 1029-8479

Publisher:: Springer Berlin

Country of Publication:: United States

Language:: English

Subject:: 72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS; 71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSICS; 97 MATHEMATICS AND COMPUTING; Mathematics

Citation Formats


                    Demirkaya, A., Decker, R., Kevrekidis, P. G., Christov, I. C., and Saxena, Avadh. Kink dynamics in a parametric Φ6 system: a model with controllably many internal modes.  United States: N. p., 2017. 
Web.  doi:10.1007/JHEP12(2017)071.

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                    Demirkaya, A., Decker, R., Kevrekidis, P. G., Christov, I. C., & Saxena, Avadh. Kink dynamics in a parametric Φ6 system: a model with controllably many internal modes.  United States.  https://doi.org/10.1007/JHEP12(2017)071

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                    Demirkaya, A., Decker, R., Kevrekidis, P. G., Christov, I. C., and Saxena, Avadh. Thu .  
"Kink dynamics in a parametric Φ6 system: a model with controllably many internal modes".  United States.  https://doi.org/10.1007/JHEP12(2017)071.  https://www.osti.gov/servlets/purl/1415382.

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@article{osti_1415382,

  title        = {Kink dynamics in a parametric Φ6 system: a model with controllably many internal modes},

  author       = {Demirkaya, A. and Decker, R. and Kevrekidis, P. G. and Christov, I. C. and Saxena, Avadh},

  abstractNote = {We explore a variant of the Φ6 model originally proposed in Phys. Rev.D 12 (1975) 1606 as a prototypical, so-called, “bag” model in which domain walls play the role of quarks within hadrons. We examine the steady state of the model, namely an apparent bound state of two kink structures. We explore its linearization, and we find that, as a function of a parameter controlling the curvature of the potential, an effectively arbitrary number of internal modes may arise in the point spectrum of the linearization about the domain wall profile. We explore some of the key characteristics of kink-antikink collisions, such as the critical velocity and the multi-bounce windows, and how they depend on the principal parameter of the model. We find that the critical velocity exhibits a non-monotonic dependence on the parameter controlling the curvature of the potential. For the multi-bounce windows, we find that their range and complexity decrease as the relevant parameter decreases (and as the number of internal modes in the model increases). We use a modified collective coordinates method [in the spirit of recent works such as Phys. Rev.D 94 (2016) 085008] in order to capture the relevant phenomenology in a semi-analytical manner.},

  doi          = {10.1007/JHEP12(2017)071},

  journal      = {Journal of High Energy Physics (Online)},

  number       = 12,

  volume       = 2017,

  place        = {United States},

  year         = {2017},

  month        = {12}

}

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Works referenced in this record:

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Gani, Vakhid A.; Lensky, Vadim; Lizunova, Mariya A.
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Sugiyama, T.
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Dorey, Patrick; Mersh, Kieran; Romanczukiewicz, Tomasz
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One-loop kink mass shifts: A computational approach
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Suppression of two-bounce windows in kink-antikink collisions
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Journal of High Energy Physics, Vol. 2016, Issue 9
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A mechanical analog of the two-bounce resonance of solitary waves: Modeling and experiment
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Goodman, Roy H.; Rahman, Aminur; Bellanich, Michael J.
Chaos: An Interdisciplinary Journal of Nonlinear Science, Vol. 25, Issue 4
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Multi-kink collisions in the ϕ 6 model
journal, July 2017

Moradi Marjaneh, Aliakbar; Gani, Vakhid A.; Saadatmand, Danial
Journal of High Energy Physics, Vol. 2017, Issue 7
DOI: 10.1007/JHEP07(2017)028

Kink–Antikink Scattering in φ ⁴ and ϕ ⁶ Models
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Works referencing / citing this record:

False vacuum decay in kink scattering
journal, October 2018

Gomes, Adalto R.; Simas, F. C.; Nobrega, K. Z.
Journal of High Energy Physics, Vol. 2018, Issue 10
DOI: 10.1007/jhep10(2018)192

Kink-Kink and Kink-Antikink Interactions with Long-Range Tails
journal, May 2019

Christov, Ivan C.; Decker, Robert J.; Demirkaya, A.
Physical Review Letters, Vol. 122, Issue 17
DOI: 10.1103/physrevlett.122.171601

Scattering of the double sine-Gordon kinks
journal, April 2018

Gani, Vakhid A.; Marjaneh, Aliakbar Moradi; Askari, Alidad
The European Physical Journal C, Vol. 78, Issue 4
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Scattering of kinks of the sinh-deformed $$\varphi ^4$$ φ 4 model
journal, April 2018

Bazeia, Dionisio; Belendryasova, Ekaterina; Gani, Vakhid A.
The European Physical Journal C, Vol. 78, Issue 4
DOI: 10.1140/epjc/s10052-018-5815-z

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

Gani, Vakhid A.; Moradi Marjaneh, Aliakbar; Saadatmand, Danial
The European Physical Journal C, Vol. 79, Issue 7
DOI: 10.1140/epjc/s10052-019-7125-5

Kink scattering in hyperbolic models
journal, November 2019

Bazeia, D.; Gomes, Adalto R.; Nobrega, K. Z.
International Journal of Modern Physics A, Vol. 34, Issue 31
DOI: 10.1142/s0217751x19502002

Scattering of the double sine-Gordon kinks
text, January 2017

Gani, Vakhid A.; Marjaneh, Aliakbar Moradi; Askari, Alidad
arXiv
DOI: 10.48550/arxiv.1711.01918

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Similar Records

Title: Kink dynamics in a parametric Φ6 system: a model with controllably many internal modes

Abstract

Citation Formats

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

Kink-Antikink Collisions in the phi^4 Equation: The n-Bounce Resonance and the Separatrix Map journal, January 2005

Kink-Antikink Collisions in the Two-Dimensional 4 Model journal, May 1979

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

One-loop kink mass shifts: A computational approach journal, November 2011

Solitons and their interactions in classical field theory journal, April 1997

Premartensitic Transition Driven by Magnetoelastic Interaction in bcc Ferromagnetic Ni 2 MnGa journal, November 1997

Classical φ6-field theory in (1+1) dimensions. A model for structural phase transitions journal, September 1980

Suppression of two-bounce windows in kink-antikink collisions journal, September 2016

A mechanical analog of the two-bounce resonance of solitary waves: Modeling and experiment journal, April 2015

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

Kink–Antikink Scattering in φ 4 and ϕ 6 Models journal, March 2014

Theory of tetragonal twin structures in ferroelectric perovskites with a first-order phase transition journal, July 1991

Solitary wave collisions revisited journal, January 1986

Vacuum polarization energy for general backgrounds in one space dimension journal, March 2017

False vacuum decay in kink scattering journal, October 2018

Kink-Kink and Kink-Antikink Interactions with Long-Range Tails journal, May 2019

Scattering of the double sine-Gordon kinks journal, April 2018

Scattering of kinks of the sinh-deformed $$\varphi ^4$$ φ 4 model journal, April 2018

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Kink scattering in hyperbolic models journal, November 2019

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Title: Kink dynamics in a parametric Φ⁶ system: a model with controllably many internal modes

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

Kink-Antikink Collisions in the phi^4 Equation: The n-Bounce Resonance and the Separatrix Map
journal, January 2005

Kink-Antikink Collisions in the Two-Dimensional 4 Model
journal, May 1979

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

One-loop kink mass shifts: A computational approach
journal, November 2011

Solitons and their interactions in classical field theory
journal, April 1997

Premartensitic Transition Driven by Magnetoelastic Interaction in bcc Ferromagnetic ${Ni}_{2} MnGa$
journal, November 1997

Classical φ6-field theory in (1+1) dimensions. A model for structural phase transitions
journal, September 1980

Suppression of two-bounce windows in kink-antikink collisions
journal, September 2016

A mechanical analog of the two-bounce resonance of solitary waves: Modeling and experiment
journal, April 2015

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

Kink–Antikink Scattering in φ ⁴ and ϕ ⁶ Models
journal, March 2014

Theory of tetragonal twin structures in ferroelectric perovskites with a first-order phase transition
journal, July 1991

Solitary wave collisions revisited
journal, January 1986

Vacuum polarization energy for general backgrounds in one space dimension
journal, March 2017

False vacuum decay in kink scattering
journal, October 2018

Kink-Kink and Kink-Antikink Interactions with Long-Range Tails
journal, May 2019

Scattering of the double sine-Gordon kinks
journal, April 2018

Scattering of kinks of the sinh-deformed $$\varphi ^4$$ φ 4 model
journal, April 2018

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

Kink scattering in hyperbolic models
journal, November 2019

Scattering of the double sine-Gordon kinks
text, January 2017