Order-chaos transitions in field theories with topological terms: A dynamical systems approach

Abstract

We present a comparative study of the dynamical behaviour of topological systems of recent interest, namely the non-Abelian Chern-Simons Higgs system and the Yang-Mills Chern-Simons Higgs system. By reducing the full field theories to temporal differential systems by using the assumption of spatially homogeneous fields, we study the Lyapunov exponents for two types of initial conditions. We also examine in minute detail the behaviour of the Lyapunov spectra as a function of the various coupling parameters in the system. We compare our results with those for Abelian Higgs, Yang-Mills Higgs and Yang-Mills Chern-Simons systems which have been discussed recently by other authors. The role of the various terms in the Hamiltonians for such systems in determining the order-disorder transitions is emphasized and shown to be counter-intuitive in the Yang-Mills Chern-Simons Higgs systems.