Kink scattering in a hybrid model

TL;DR

This paper investigates kink scattering in a hybrid model with two topological sectors, revealing new bounce window structures, sector-changing oscillations, and the dynamics of kink interactions, extending known results from the $bbeta;\u03b4;b4$ model.

Contribution

It introduces a hybrid model with dual topological sectors, analyzes kink scattering dynamics, and uncovers novel bounce structures and sector-changing phenomena.

Findings

New bounce window structures in kink-antikink collisions.

Oscillations and topological sector changes during scattering.

Kink-kink interactions are purely repulsive with no bound states.

Abstract

In this work we consider a model where the potential has two topological sectors connecting three adjacent minima, as occurs with the $\phi^6$ model. In each topological sector, the potential is symmetric around the local maximum. For $\phi>0$ there is a linear map between the model and the $\lambda\phi^4$ model. For $\phi<0$ the potential is reflected. Linear stability analysis of kink and antikink lead to discrete and continuum modes related by a linear coordinate transformation to those known analytically for the $\lambda\phi^4$ model. Fixing one topological sector, the structure of antikink-kink scattering is related to the observed in the $\lambda\phi^4$ model. For kink-antikink collisions a new structure of bounce windows appear. Depending on the initial velocity, one can have oscillations of the scalar field at the center of mass even for one bounce, or a change of topological sector. We also found a structure of one-bounce, with secondary windows corresponding to the changing of the topological sector accumulating close to each one-bounce windows. The kink-kink collisions are characterized by a repulsive interaction and there is no possibility of forming a bound state.