Scattering of Vortices with Excited Normal Modes

TL;DR

This paper studies head-on vortex collisions in the Abelian-Higgs model, revealing complex behaviors like trapping and fractal scattering patterns when vortices are excited by normal modes.

Contribution

It introduces analysis of vortex scattering with excited normal modes, showing failure of the moduli space approximation and discovering fractal scattering structures.

Findings

Vortices can become trapped in quasi-bound states.

Fractal structures depend on initial phase and velocity.

Normal mode excitation significantly affects vortex dynamics.

Abstract

We consider head-on collisions at critical coupling of vortices modelled by the Abelian-Higgs model. We investigate the 2-vortex scattering, whereby the vortices are excited by the shape mode causing fluctuations in the gauge-invariant quantities. When the vortices are excited with a sufficiently large amplitude the moduli space approximation fails, and we observe an interesting behaviour in which the vortices can become trapped in a quasi-bound state with multiple bounces. We perform a detailed investigation on the behaviour of these excited vortices and sample a phase space of solutions. Interestingly, we find a fractal structure dependent on the initial phase of the mode and velocity of the vortices.