Quantum signature of the chaos-order transition in a homogeneous SU(2) Yang-Mills-Higgs system

We analyze a spatially homogeneous SU(2) Yang-Mills-Higgs system both in cl assical and in quantum mechanics. By using the Toda criterion of the Gaussi an curvature, we find a classical chaos-order transition as a function of t he Higgs vacuum, the Yang-Mills coupling constant, and the energy of the sy stem. We then study the nearest neighbor spacing distribution of the energy levels, which shows a Wigner-Poisson transition by increasing the value of the Higgs held in the vacuum. This transition is a quantum signature of th e classical chaos-order transition of the system.