Chaos in the SU(2) Yang-Mills Chern-Simons matrix model

We study the effects of addition of the Chern-Simons (CS) term in the minimal Yang-Mills (YM) matrix model composed of two 2 x 2 matrices with SU(2) gauge and SO(2) global symmetry. We obtain the Hamiltonian of this system in appropriate coordinates and demonstrate that its dynamics is sensitive to the values of both the CS coupling, kappa, and the conserved conjugate momentum, p(phi), associated to the SO(2) symmetry. We examine the behavior of the emerging chaotic dynamics by computing the Lyapunov exponents and plotting the Poincare sections as these two parameters are varied and, in particular, find that the largest Lyapunov exponents evaluated within a range of values of kappa are above what is computed at kappa = 0, for kappa p(phi) < 0. We also give estimates of the critical exponents for the Lyapunov exponent as the system transits from the chaotic to nonchaotic phase with p(phi) approaching to a critical value.

Automated summary

The study examines the sensitivity of dynamics in a minimal Yang-Mills matrix model with the addition of a Chern-Simons term, showing that the system is influenced by the CS coupling and conserved conjugate momentum values. By computing Lyapunov exponents and plotting Poincare sections, the research explores the emerging chaotic dynamics and observes an increase in Lyapunov exponents with non-zero kappa values. Additionally, estimates are given for critical exponents as the system transitions from chaotic to nonchaotic phases with approaching critical values of the conjugate momentum.