Abstract
We consider a class of topological defects in (1, 1)-dimensions with a deformed ϕ 4 kink structure whose stability analysis leads to a Schrödinger-like equation with a zero-mode and at least one vibrational (shape) mode. We are interested in the dynamics of kink-antikink collisions, focusing on the structure of two-bounce windows. For small deformation and for one or two vibrational modes, the observed two-bounce windows are explained by the standard mechanism of a resonant effect between the first vibrational and the translational modes. With the increasing of the deformation, the effect of the appearance of more than one vibrational mode is the gradual disappearance of the initial two-bounce windows. The total suppression of two-bounce windows even with the presence of a vibrational mode offers a counterexample from what expected from the standard mechanism. For extremely large deformation the defect has a 2-kink structure with one translational and one vibrational mode, and the standard structure of two-bounce windows is recovered.
Article PDF
Similar content being viewed by others
Avoid common mistakes on your manuscript.
References
T. Dauxois and M. Peyrard, Physics of Solitons, Cambridge University Press, Cambridge (2006).
N. Manton and P. Sutcliffe, Topological Solitons, Cambridge University Press, Cambridge (2004).
P.P. Avelino, J.P.M. de Carvalho, C.J.A.P. Martins and J.C.R.E. Oliveira, Can our universe be inomogeneous on large subhorizon scales?, Phys. Lett. B 515 (2001) 148 [astro-ph/0004227] [INSPIRE].
Ya.B. Zel’dovich, I.Yu. Kobzarev and L.B. Okun, Cosmological Consequences of the Spontaneous Breakdown of Discrete Symmetry, Zh. Eksp. Teor. Fiz. 67 (1974) 3 [Sov. Phys. JETP 40 (1975) 1] [INSPIRE].
S.W. Hawking, I.G. Moss and J.M. Stewart, Bubble Collisions in the Very Early Universe, Phys. Rev. D 26 (1982) 2681 [INSPIRE].
M. Bucher, A Brane world universe from colliding bubbles, Phys. Lett. B 530 (2002) 1 [hep-th/0107148] [INSPIRE].
J. Braden, J.R. Bond and L. Mersini-Houghton, Cosmic bubble and domain wall instabilities I: parametric amplification of linear fluctuations, JCAP 03 (2015) 007 [arXiv:1412.5591] [INSPIRE].
A.E. Kudryavtsev, Solitonlike solutions for a Higgs scalar field, JETP Lett. 22 (1975) 82.
T. Sugiyama, Kink-Antikink Collisions in the Two-Dimensional ϕ 4 Model, Prog. Theor. Phys. 61 (1979) 1550 [INSPIRE].
M. Moshir, Soliton-antisoliton scattering and capture in λφ 4 theory, Nucl. Phys. B 185 (1981) 318 [INSPIRE].
C.A. Wingate, Numerical Search for a ϕ 4 Breather Mode, SIAM J. Appl. Math. 43 (1983) 120.
T.I. Belova and A.E. Kudryavtsev, Quasi-periodic orbits in the scalar classical λϕ 4 field theory, Physica D 32 (1988) 18.
D.K. Campbell, J.S. Schonfeld and C.A. Wingate, Resonance Structure in Kink-antikink interactions in ϕ 4 theory, Physica D 9 (1983) 1.
D.K. Campbell, M. Peyrard and P. Soldano, Kink-antikink interactions in the double sine-Gordon equation, Physica D 19 (1986) 165 [INSPIRE].
D.K. Campbell and M. Peyrard, Solitary wave collisions revisited, Physica D 18 (1986) 47 [INSPIRE].
P. Anninos, S. Oliveira and R.A. Matzner, Fractal structure in the scalar λ(φ 2 − 1)2 theory, Phys. Rev. D 44 (1991) 1147 [INSPIRE].
V.A. Gani and A.E. Kudryavtsev, Kink-antikink interactions in the double sine-Gordon equation and the problem of resonance frequencies, Phys. Rev. E 60 (1999) 3305 [cond-mat/9809015] [INSPIRE].
R.H. Goodman and R. Haberman, Kink-Antikink Collisions in the ϕ 4 Equation: The n-Bounce Resonance and the Separatrix Map, SIAM J. Appl. Dyn. Syst. 4 (2005) 1195.
V.A. Gani, V. Lensky and M.A. Lizunova, Kink excitation spectra in the (1 + 1)-dimensional φ 8 model, JHEP 08 (2015) 147 [arXiv:1506.02313] [INSPIRE].
S. Aubry, Unified approach to interpretation of displacive and order-disorder systems. II. Displacive systems, J. Chem. Phys. 64 (1976) 3392.
Z. Fei, L. Vázquez and Y.S. Kivshar, Resonant kink impurity interactions in the ϕ 4 model, Phys. Rev. A 46 (1992) 5214 [INSPIRE].
Z. Fei, Y.S. Kivshar and L. Vázquez, Resonant kink-impurity interactions in the sine-Gordon model, Phys. Rev. A 45 (1992) 6019.
Y.S. Kivshar, Z. Fei and L. Vázquez, Resonant soliton-impurity interactions, Phys. Rev. Lett. 67 (1991) 1177 [INSPIRE].
R.H. Goodman and R. Haberman, Interaction of sine-Gordon kinks with defects: The two-bounce resonance, Physica D 195 (2004) 303.
J. Yang and Y. Tan, Fractal structure in the collision of vector solitons, Phys. Rev. Lett. 85 (2000) 3624.
Y. Tan and J. Yang, Complexity and regularity of vector-soliton collisions, Phys. Rev. E 64 (2001) 056616.
R.H. Goodman and R. Haberman, Vector soliton interactions in birefringent optical fibers, Phys. Rev. E 71 (2005) 055065.
T.I. Belova and A.E. Kudryavtsev, Solitons and their interactions in classical field theory, Phys. Usp. 40 (1997) 359 [Usp. Fiz. Nauk 167 (1997) 377] [INSPIRE].
P. Dorey, K. Mersh, T. Romanczukiewicz and Y. Shnir, Kink-antikink collisions in the ϕ 6 model, Phys. Rev. Lett. 107 (2011) 091602 [arXiv:1101.5951] [INSPIRE].
V.A. Gani, A.E. Kudryavtsev and M.A. Lizunova, Kink interactions in the (1 + 1)-dimensional ϕ 6 model, Phys. Rev. D 89 (2014) 125009 [arXiv:1402.5903] [INSPIRE].
A. de Souza Dutra, Continuously deformable topological structure, Physica D 238 (2009) 798.
D. Bazeia, J. Menezes and R. Menezes, New global defect structures, Phys. Rev. Lett. 91 (2003) 241601 [hep-th/0305234] [INSPIRE].
E.B. Bogomolny, Stability of Classical Solutions, Sov. J. Nucl. Phys. 24 (1976) 449 [INSPIRE].
M.K. Prasad and C.M. Sommerfield, An Exact Classical Solution for the ’t Hooft Monopole and the Julia-Zee Dyon, Phys. Rev. Lett. 35 (1975) 760 [INSPIRE].
J.-L. Gervais and B. Sakita, Extended Particles in Quantum Field Theories, Phys. Rev. D 11 (1975) 2943 [INSPIRE].
J.-L. Gervais, A. Jevicki and B. Sakita, Perturbation Expansion Around Extended Particle States in Quantum Field Theory, Phys. Rev. D 12 (1975) 1038 [INSPIRE].
N.H. Christ and T.D. Lee, Quantum Expansion of Soliton Solutions, Phys. Rev. D 12 (1975) 1606 [INSPIRE].
T.S. Mendonça and H.P. de Oliveira, A note about a new class of two-kinks, JHEP 06 (2015) 133 [arXiv:1504.07315] [INSPIRE].
T.S. Mendonça and H.P. de Oliveira, The collision of two-kinks defects, JHEP 09 (2015) 120 [arXiv:1502.03870] [INSPIRE].
Open Access
This article is distributed under the terms of the Creative Commons Attribution License (CC-BY 4.0), which permits any use, distribution and reproduction in any medium, provided the original author(s) and source are credited.
Author information
Authors and Affiliations
Corresponding author
Additional information
ArXiv ePrint: 1605.05344
Rights and permissions
Open Access This article is distributed under the terms of the Creative Commons Attribution 4.0 International License (https://creativecommons.org/licenses/by/4.0), which permits use, duplication, adaptation, distribution, and reproduction in any medium or format, as long as you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons license, and indicate if changes were made.
About this article
Cite this article
Simas, F.C., Gomes, A.R., Nobrega, K.Z. et al. Suppression of two-bounce windows in kink-antikink collisions. J. High Energ. Phys. 2016, 104 (2016). https://doi.org/10.1007/JHEP09(2016)104
Received:
Revised:
Accepted:
Published:
DOI: https://doi.org/10.1007/JHEP09(2016)104