The decay of Hopf solitons in the Skyrme model

TL;DR

This paper investigates the decay process of Hopf solitons in the Skyrme model, revealing their instability, decay dynamics, and radiation emission through a novel numerical method.

Contribution

It introduces a matrix-free numerical approach to study the decay of Hopf solitons and analyzes their radiation emission during decay.

Findings

Hopf solitons are unstable and decay to the vacuum.

Decay involves emission of isospinning radiation.

Developed a new numerical method for energy Hessian analysis.

Abstract

It is understood that the Skyrme model has a topologically interesting baryonic excitation which can model nuclei. So far no stable knotted solutions, of the Skyrme model, have been found. Here we investigate the dynamics of Hopf solitons decaying to the vacuum solution in the Skyrme model. In doing this we develop a matrix-free numerical method to identify the minimum eigenvalue of the Hessian of the corresponding energy functional. We also show that as the Hopf solitons decay, they emit a cloud of isospinning radiation.