Numerical investigation for the properties of nonintegrable quantum systems eigenspace in the line of quantum-classical correspondence

The properties of the eigenspace of nonintegrable quantum systems are explo red in detail in the light of the viewpoint of quantum-classical completely correspondence proposed recently by Xu et al. The changes of the topologic al structure in the state space of autonomous quantum system due to the non linear resonance are displayed numerically with the uncertainty measure of a special initial state rho (alpha)(lambda) and the transformation matrix U (lambda + delta lambda,lambda -delta lambda). The statistical behavior of t he subspace occupied by the state in eigenspace of quantum nonintegrable sy stem is discussed carefully with the help of a special renormalization meth od. The results show that the randomness of effective Hamiltonian matrix, t he transition matrix and the nearest level spacings in;this region can be d escribed by random matrix theory. And the extent of agreement of our calcul ation with the prediction of GOE is in correspondence to the extent of the classical torus violation.