A toy model to explain the missing bounce windows in the kink-antikink collisions

TL;DR

This paper introduces a simplified model to explain the absence of certain bounce windows in kink-antikink collisions within a specific field theory, highlighting the role of mode coupling in this phenomenon.

Contribution

It presents a novel toy model that captures the fractal collision structure and elucidates the mechanism behind missing bounce windows in $$ theory.

Findings

The toy model reproduces the fractal collision pattern.

Missing bounce windows are linked to mode coupling.

Two bounce resonance aligns with the lower eigenfrequency.

Abstract

We propose a toy model to reproduce the fractal structure of kink and antikink collisions on one topological sector of $\phi^6$ theory. Using the toy model, we investigate the missing bounce windows observed in the fractal structure, and show that the coupling between two oscillation modes modulate the emergence of the missing bounce windows. By numerical calculation, we present that the two bounce resonance corresponds to the lower eigenfrequency of the toy model.