Kink-antikink collisions in a weakly interacting $\phi^4$ model

TL;DR

This paper investigates how varying the static intersoliton force in a modified $^4$ model affects kink-antikink collision dynamics, revealing the transition from thin to thick spectral walls as the force strength changes.

Contribution

It introduces a parameterized $^4$ model to study the impact of static intersoliton forces on collision dynamics and spectral wall formation.

Findings

Spectral walls broaden from thin to thick with increasing static force.

Discrete mode crossing into the continuum influences soliton collision outcomes.

Spectral wall phenomena are observable across different force regimes.

Abstract

We study kink-antikink scattering in a one-parameter variant of the $\phi^4$ theory where the model parameter controls the static intersoliton force. We interpolate between the limit of no static force (BPS limit) and the regime where the static interaction is small (non-BPS). This allows us to study the impact of the strength of the intersoliton static force on the soliton dynamics. In particular, we analyze how the transition of a bound mode through the mass threshold affects the soliton dynamics in a generic process, i.e., when a static intersoliton force shows up. We show that the thin, precisely localized spectral wall which forms in the limit of no static force, broadens in a well-defined manner when a static force is included, giving rise to what we will call a thick spectral wall. This phenomenon just requires that a discrete mode crosses into the continuum at some intermediate stage of the dynamics and, therefore, should be observable in many soliton-antisoliton collisions.