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 classical and quantum mechanics. By using the Toda criterion of the Gaussian curvature we find a classical chaos-order transition as a function of the Higgs vacuum, the Yang-Mills coupling constant and the energy of the system. Then, we study the nearest-neighbour spacing distribution of the energy levels, which shows a Wigner-Poisson transition by increasing the value of the Higgs field in the vacuum. This transition is a clear quantum signature of the classical chaos-order transition of the system.