Multikink scattering in the $\phi^6$ model revisited

TL;DR

This paper investigates antikink-kink collisions in the $^6$ model, providing evidence that energy transfer occurs to a collective bound mode and developing a collective coordinate model that accurately reproduces the scattering dynamics.

Contribution

The study confirms the role of a collective bound mode in $ar{ m K} { m K}$ scattering and introduces a CCM that accurately models the full dynamics, including radiation effects.

Findings

Energy is transferred to a collective bound mode during scattering.

The CCM reproduces the full scattering dynamics with high accuracy.

Radiation significantly influences kink-antikink interactions.

Abstract

Antikink-kink ( $\bar{\rm K} $$ {\rm K}$) collisions in the $\phi^6$ model exhibit resonant scattering although the $\phi^6$ kinks do not support any bound states to which energy could be transferred. In Phys. Rev. Lett. 107 (2011) 091602 it was conjectured that, instead, energy is transferred to a collective bound mode of the full $\bar{\rm K} $$ {\rm K}$ configuration. Here we present further strong evidence for this conjecture. Further, we construct a collective coordinate model (CCM) for $\bar{\rm K} $$ {\rm K}$ scattering based on this collective bound mode trapped between the $\bar{\rm K} $$ {\rm K}$ pair which allows us to reproduce the full dynamics of $\bar{\rm K} $$ {\rm K}$ scattering with striking accuracy. We also study kink-antikink (${\rm K} $$ \bar{\rm K}$) scattering and its description by a CCM. In this case a significant role of radiation is discovered.