Radial vibrations of BPS skyrmions

TL;DR

This paper investigates the radial vibrational modes of spherically symmetric skyrmions within the BPS Skyrme model, combining linear and nonlinear numerical analyses to identify resonances that correspond well with experimental data.

Contribution

It provides the first detailed numerical analysis of radial vibrations in BPS skyrmions, linking these excitations to physical resonances like the Roper resonance.

Findings

Fundamental excitation matches Roper resonance.

Higher resonances appear for various potentials.

Linear and nonlinear analyses agree on resonance properties.

Abstract

We study radial vibrations of spherically symmetric skyrmions in the BPS Skyrme model. Concretely, we numerically solve the linearised field equations for small fluctuations in a skyrmion background, both for linearly stable oscillations and for (unstable) resonances. This is complemented by numerical solutions of the full nonlinear system, which confirm all the results of the linear analysis. In all cases, the resulting fundamental excitation provides a rather accurate value for the Roper resonance, supporting the hypothesis that the BPS Skyrme model already gives a reasonable approximate description of this resonance. Further, for many potentials additional higher resonances appear, again in agreement with known experimental results.