Dynamics of Excited BPS 3-Vortices

TL;DR

This paper investigates the dynamics of BPS 3-vortex solutions, analyzing their moduli space, collision behaviors, and how vibrational excitations lead to chaotic multi-bounce interactions.

Contribution

It provides a detailed study of the moduli space and vibrational modes of 3-vortex solutions, revealing how shape excitations induce chaotic scattering patterns.

Findings

Identified geodesic scattering angles of 90° and 60° for specific vortex configurations.

Analyzed vibrational spectra showing how shape modes modify vortex interactions.

Demonstrated transition from free motion to chaos due to shape mode excitations.

Abstract

We analyze the dynamics of BPS 3-vortex solutions. First, for unexcited vortices, we study the 2-dimensional moduli space of centred vortices with $y \to -y$ symmetry, and its metric. We identify the 1-dimensional subspaces describing the head-on collisions of equidistant collinear and equilateral triangle configurations, where geodesic motion results in $90^\circ$ and 60^\circ$ scattering, respectively. Second, by studying the frequency spectrum of vibrational shape modes along these subspaces, we explain how the force-free, geodesic motion is modified by shape mode excitations into a pattern of chaotic multi-bounce collisions.