Order-chaos transitions in field theories with topological terms: a dynamical systems approach
arXiv:hep-th/9610071 · doi:10.1088/0305-4470/30/9/014
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 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.
19 pages,15 figures available in hard copy from C. Mukku, and through e-mail from [email protected]. To appear in J. Phys. A