Internal Excitations of Global Vortices

TL;DR

This paper studies the internal excitation modes of global vortices in 2+1 dimensions, analyzing their spectrum, decay, and excitation through simulations in various physical scenarios, including cosmological backgrounds.

Contribution

It provides a detailed numerical analysis of vortex internal modes, their excitation, decay, and energy storage capacity in different physical contexts, including cosmology.

Findings

Localized excitation modes exist in global vortices.

Vortices can be excited by external sources but do not store large energy in these modes.

Energy in vortex excitations remains below 1% of vortex core mass in cosmological evolution.

Abstract

We investigate the spectrum of linearized excitations of global vortices in $2+1$ dimensions. After identifying the existence of localized excitation modes, we compute the decay time scale of the first two and compare the results to the numerical evolution of the full non-linear equations. We show numerically how the interaction of vortices with an external source of radiation or other vortices can excite these modes dynamically. We then simulate the formation of vortices in a phase transition and their interaction with a thermal bath estimating the amplitudes of these modes in each case. These numerical experiments indicate that even though, in principle, vortices are capable of storing a large amount of energy in these internal excitations, this does not seem to happen dynamically. We then explore the evolution of a network of vortices in an expanding (2+1) dimensional background, in particular in a radiation dominated universe. We find that vortices are still excited after the course of the cosmological evolution but again the level of excitation is very small. The extra energy in the vortices in these cosmological simulations never exceeds the $1\%$ level of the total mass of the core of the vortex.