Kink-antikink collisions in the $\phi^8$ model: short-range to long-range journey

TL;DR

This paper provides a comprehensive analysis of kink-antikink collisions in the $$ model, revealing how the transition from short-range to long-range interactions affects collision dynamics and radiation emission.

Contribution

It offers the first exhaustive simulation-based study of all collision sectors in the $$ model, including the effects of merging minima on kink interactions.

Findings

Resonance windows observed in all sectors.

Long-range tails lead to direct radiation decay.

Merging minima alter collision outcomes and kink behavior.

Abstract

We studied kink-antikink collisions in (1+1)-dimensional spacetime for all $Z_2$ symmetric $\phi^8$ models with four degenerate minima. Such a polynomial model has only one free parameter, allowing us to conduct an exhaustive analysis. We performed detailed simulations in all three sectors of the model. We observed resonance windows from both localized and delocalized modes, as well as a sector change with the formation of additional kink-antikink pairs. Furthermore, we were able to show how collisions are modified when two quadratic minima merge into a quartic one, causing the kinks to acquire a long-range character. We demonstrated that when the tail not facing the opposing kink is long-range, incoming kinks and antikinks decay directly into radiation, as suggested in \cite{campos2021interaction}, by forming a large number of small kink-antikink pairs. Finally, we briefly discussed whether our analysis could be generalized to other polynomial models.