Regular and chaotic interactions of two BPS dyons at low energy

TL;DR

This paper investigates the complex dynamics of two BPS dyons at low energy, revealing quasiperiodic and chaotic behaviors through numerical analysis within a simplified geodesic approximation.

Contribution

It is the first detailed numerical study of chaotic and quasiperiodic interactions in BPS dyon pairs using phase space analysis tools.

Findings

Evidence of quasiperiodic motion in BPS dyons

Detection of chaotic behavior in dyon interactions

Quantitative characterization of dynamics via Lyapunov exponents

Abstract

We identify and analyze quasiperiodic and chaotic motion patterns in the time evolution of a classical, non-Abelian Bogomol'nyi-Prasad-Sommerfield (BPS) dyon pair at low energies. This system is amenable to the geodesic approximation which restricts the underlying SU(2) Yang-Mills-Higgs dynamics to an eight-dimensional phase space. We numerically calculate a representative set of long-time solutions to the corresponding Hamilton equations and analyze quasiperiodic and chaotic phase space regions by means of Poincare surfaces of section, high-resolution power spectra and Lyapunov exponents. Our results provide clear evidence for both quasiperiodic and chaotic behavior and characterize it quantitatively. Indications for intermittency are also discussed.