Chaos in Abelian and non-Abelian Higgs systems

Abstract

The nonintegrability and chaotic nature of the Yang-Mills Higgs systems are considered. We have studied the Abelian Higgs model and the SO(3) Georgi-Glashow model (non-Abelian Higgs model), which possess vortices and monopole solutions respectively. The Painlevé analysis of the corresponding time-dependent equations of motion shows that both systems are nonintegrable for all choices of the parameter values. The Poincare surface-of-section plot shows the presence of chaotic trajectories in the phase space at certain parameter values for both systems. The chaotic nature of the trajectories is also indicated by the computations of the Lyapunov exponents of the corresponding systems.