Exact oscillations and chaos on a non-Abelian coil

TL;DR

This paper presents exact time-periodic solutions in the Georgi-Glashow model that exhibit stationary energy density and resonances, revealing a transition from oscillatory to chaotic behavior at higher energies.

Contribution

It introduces new exact solutions called non-Abelian self-sustained coils and analyzes their transition to chaos using various dynamical methods.

Findings

Existence of exact time-periodic solutions with stationary energy density.

Identification of a transition to chaos at higher energies.

Characterization of chaos through Poincaré sections, Fourier spectra, and geodesic deviation growth.

Abstract

We construct new exact solutions of the Georgi-Glashow model in $3+1$ dimensions. These configurations are periodic in time but lead to a stationary energy density and no energy flux. Nevertheless, they possess a characteristic frequency which manifests itself through non-trivial resonances on test fields. This allows us to interpret them as non-Abelian self sustained coils. We show that for larger energies a transition to chaotic behavior takes place, which we characterize by Poincar\'e sections, Fourier spectra and exponential growth of the geodesic deviation in an effective Jacobi metric, the latter triggered by parametric resonances.