QUANTUM-STATISTICAL RELAXATION IN A CLASSICALLY CHAOTIC SYSTEM

Classical statistical relaxation is quantitatively characterized by th e ergodicity, an important relation connecting the time-averaged and e nsemble-averaged properties of dynamical observables. In principle, th e quantum statistical relaxation should be characterized corresponding ly by the quantum ergodicity. In this paper, we have theoretically sho wn that quantum ergodicity can only be realized under the condition M much greater than Delta N much greater than 1, and this condition can be readily satisfied as the effective Planck constant (h) over tilde a pproaches 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.