Kink-antikink collision in a Lorentz-violating ${\varphi }^4$ model

Abstract

In this work, kink-antikink collision in a two-dimensional Lorentz-violating ${\varphi }^4$ model is considered. It is shown that the Lorentz-violating term in the proposed model does not affect the structure of the linear perturbation spectrum of the standard ${\varphi }^4$ model, and thus there exists only one vibrational mode. The Lorentz-violating term impacts, however, the frequency and spatial wave function of the vibrational mode. As a consequence, the well-known results on ${\varphi }^4$ kink-antikink collision will also change. Collisions of kink-antikink pairs with different values of initial velocities and Lorentz-violating parameters are simulated using the Fourier spectral method. Our results indicate that models with larger Lorentz-violating parameters would have smaller critical velocities $v_c$ and smaller widths of bounce windows. Interesting fractal structures existing in the curves of maximal energy densities of the scalar field are also found.

arXiv comment8 pages, 9 figures, final version published by Phys. Lett. B

References in corpus (54)

• A Large Mass Hierarchy from a Small Extra Dimension
• An Alternative to Compactification
• The Hierarchy Problem and New Dimensions at a Millimeter
• Data Tables for Lorentz and CPT Violation
• The Einstein Equations on the 3-Brane World
• Modern tests of Lorentz invariance
• Noncommutative Field Theory and Lorentz Violation
• Signals for Lorentz Violation in Electrodynamics
• Stability, Causality, and Lorentz and CPT Violation
• Tests of Lorentz invariance: a 2013 update
• Thick brane solutions
• Kink-antikink collisions in the phi^6 model
• An Early Proposal of "Brane World"
• Supersymmetry and Lorentz Violation
• Kink interactions in the (1+1)-dimensional ${\phi }^6$ model
• Kink-kink and kink-antikink interactions with long-range tails
• Kink-antikink interactions in the double sine-Gordon equation and the problem of resonance frequencies
• Long-range interactions of kinks
• Kink excitation spectra in the (1+1)-dimensional ${\phi }^8$ model
• Scattering of the ${\phi }^8$ kinks with power-law asymptotics
• Spectral Walls in Soliton Collisions
• Scattering of kinks of the sinh-deformed ${\phi }^4$ model
• Scattering of the double sine-Gordon kinks
• Resonant kink-antikink scattering through quasinormal modes
• Defect Structures in Lorentz and CPT Violating Scenarios
• Multi-kink collisions in the ${\varphi }^6$ model
• Constraints on Lorentz invariance violation from gamma-ray burst GRB090510
• Kink-Antikink Collisions and Multi-Bounce Resonance Windows in Higher-Order Field Theories
• Multi-kink scattering in the double sine-Gordon model
• Reflection, transmutation, annihilation and resonance in two-component kink collisions
• Information-Entropic for Travelling Solitons in Lorentz and CPT Breaking Systems
• Cosmic Rays and the Search for a Lorentz Invariance Violation
• Lorentz-violating effects on topological defects generated by two real scalar fields
• High energy density in the collision of $N$ kinks in the ${\varphi }^4$ model
• Kink dynamics in a system of two coupled scalar fields in two space-time dimensions
• Traveling solitons in Lorentz-violating systems
• Lorentz violation dispersion relation and its application
• Kink-antikink scattering in the ${\varphi }^4$ model without static intersoliton forces
• Extreme values of elastic strain and energy in sine-Gordon multi-kink collisions
• Kink scattering in a hybrid model
• Collision of two kinks with inner structure
• High energy density in multi-soliton collisions
• Kink scattering in hyperbolic models
• Kink dynamics in the MSTB Model
• Neutrino Oscillations and Lorentz Invariance Violation
• False vacuum decay in kink scattering
• Asymmetric kink scattering in a two-component scalar field theory model
• Kink-antikink collisions for twin models
• $K$-field kinks: stability, exact solutions and new features
• Kinks in higher derivative scalar field theory
• The collision of two-kinks revisited: the creation of kinks and lump-like defects as metastable states
• Kondo effect from a Lorentz-violating domain wall description of superconductivity
• Searching for Lorentz Violation
• Lorentz Violation and Topologically Trapped Charge Carriers in 2D Materials

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