Kink-antikink collision in a Lorentz-violating ϕ4 model

Abstract

In this work, kink-antikink collision in a two-dimensional Lorentz-violating ϕ4 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 ϕ4 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 ϕ4 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 vc and smaller widths of bounce windows. Interesting fractal structures existing in the curves of maximal energy densities of the scalar field are also found.

Keywords

• Kink collision
• Lorentz-violating models
• Spectral methods