Quantum Signature of the Chaos-Order Transition in a Homogeneous SU(2) Yang-Mills-Higgs System

TL;DR

This paper investigates the classical and quantum chaos-order transition in a homogeneous SU(2) Yang-Mills-Higgs system, revealing a quantum signature through energy level statistics that correlates with classical behavior.

Contribution

It demonstrates a quantum signature of the classical chaos-order transition via energy level spacing analysis in a Yang-Mills-Higgs system.

Findings

Classical chaos-order transition identified using Toda criterion.

Quantum energy level statistics show Wigner-Poisson transition.

Quantum signatures correlate with classical chaos in the system.

Abstract

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.