# Kink dynamics in a parametric *Φ* ^{6} system: a model with controllably many internal modes

## Abstract

We explore a variant of the *Φ* ^{6} 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:

- 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:

- 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:
- Journal Article: 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.

```
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. doi:10.1007/JHEP12(2017)071.

```
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.
doi:10.1007/JHEP12(2017)071. https://www.osti.gov/servlets/purl/1415382.
```

```
@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 = {Thu Dec 14 00:00:00 EST 2017},

month = {Thu Dec 14 00:00:00 EST 2017}

}