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

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 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 and contrast our results with those for Abelian Higgs, Yang-Mills Higgs and Yang-Mills Chern-Simons systems which have been discussed by other authors recently. 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.