Quantum statistical relaxation in a classically chaotic system

Classical statistical relaxation is quantitatively characterized by the ergodicity, an important relation connecting the time-averaged and ensemble-averaged properties of dynamical observables. In principle, the quantum statistical relaxation should be characterized correspondingly by the quantum ergodicity. In this paper, we have theoretically shown that quantum ergodicity can only be realized under the condition M ⪢ ΔN ⪢ 1, and this condition can be readily satisfied as the effective Planck constant approaches zero. These theoretical results are numerically testified in a nuclear model, known as a three-level Lipkin model whose classical counterpart can exhibit classical chaos.