Chaotic thermalization in Yang-Mills-Higgs theory on a spacial lattice

We analyze the Hamiltonian time evolution of classical SU(2) Yang-Mills-Higgs theory with a fundamental Higgs doublet on a spacial lattice. In particular, we study energy transfer and equilibration processes among the gauge and Higgs sectors, calculate the maximal Lyapunov exponents under randomized initial conditions in the weak-coupling regime, where one expects them to be related to the high-temperature plasmon damping rate, and investigate their energy and coupling dependence. We further examine finite-time and finite-size errors, study the impact of the Higgs fields on the instability of constant non-Abelian magnetic fields, and comment on the implications of our results for the thermalization properties of hot gauge fields in the presence of matter.