Collective Coordinate Models for 2-Vortex Shape Mode Dynamics

TL;DR

This paper develops models for charge-2 Abelian Higgs vortex dynamics, incorporating shape mode oscillations, revealing complex behaviors like chaos and fractal structures in vortex collisions.

Contribution

It introduces a new model that extends geodesic flow on the moduli space by including shape mode effects, capturing chaotic vortex interactions.

Findings

Fast mode oscillations lead to geodesic flow with potential modifications.

Large amplitude shape modes induce chaotic vortex collision dynamics.

Predicted fractal structures in vortex-vortex collision outcomes.

Abstract

Models are developed for the motion of charge-2 Abelian Higgs vortices through the 2-vortex moduli space $M$, with the vortices excited by their shape mode oscillations. The models simplify to the well-known geodesic flow on $M$, modified by a potential, when the mode oscillations are fast relative to the moduli space motion and their amplitudes are small. When the lowest-frequency mode is excited with a large amplitude, the geodesic flow is not a correct description. Instead, a chaotic, or even fractal, multi-bounce structure in vortex-vortex collisions is predicted.