Planar Skyrmions: Vibrational Modes and Dynamics

TL;DR

This paper investigates the vibrational modes and collision dynamics of planar Skyrmions in a (2+1)-dimensional Skyrme model, revealing complex scattering behaviors influenced by internal modes and a parameter alpha.

Contribution

It classifies and computes the vibrational spectrum of Skyrmions across different alpha values, uncovering fractal-like scattering structures.

Findings

Skyrmion collisions depend on alpha and incident speed.

Internal vibrational modes significantly influence scattering outcomes.

Fractal scattering windows similar to kink-antikink phenomena are observed.

Abstract

We study Skyrmion dynamics in a (2+1)-dimensional Skyrme model. The system contains a dimensionless parameter alpha, with alpha=0 corresponding to the O(3) sigma-model. If two Skyrmions collide head-on, then they can either coalesce or scatter -- this depends on alpha and on the incident speed v, and is affected by transfer of energy to and from the internal vibrational modes of the Skyrmions. We classify these internal modes and compute their spectrum, for a range of values of alpha. In particular, we find that there is a fractal-like structure of scattering windows, analogous to those seen for kink-antikink scattering in 1+1 dimensions.