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

TL;DR

This paper investigates the dynamical behavior and order-chaos transitions in topological field theories, specifically Chern-Simons Higgs systems, using a dynamical systems approach and Lyapunov exponents analysis.

Contribution

It provides a comparative analysis of non-Abelian and Yang-Mills Chern-Simons Higgs systems, highlighting the role of Hamiltonian terms in order-disorder transitions.

Findings

Lyapunov spectra vary with coupling parameters

Order-chaos transitions depend on Hamiltonian terms

Counter-intuitive effects observed in Yang-Mills Chern-Simons systems

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.