Quantum chaoticity and fractional parentage plot based on the microscopic theory of nuclear collective dynamics

Being based on the dynamical theory of nuclear collective dynamics, in the previous paper, we have proposed a general method for evaluating the stochasticity of individual eigenfunctions. It has been demonstrated that an onset of quantum chaos is induced by a dissolution of quantum numbers, which is accompanied by the violation of separability condition for an optimum collective subspace. On the other hand, there exists a well established method for analyzing the stochasticity of an ensemble of eigenstates, i.e. the level statistics based on the random matrix theory which is based on some probabilistic assumptions. It is the objective of the present paper to build a bridge between the two different approaches to the quantum chaos, with and without probabilistic assumptions. (author)