Numerical Investigation for the Properties of Nonintegrable Quantum Systems Eigenspace in the Line of Quantum-Classical Correspondence**The project supported by National Natural Science Foundation of China

Abstract

The properties of the eigenspace of nonintegrable quantum systems are explored in detail in the light of the viewpoint of quantum-classical completely correspondence proposed recently by Xu et al. The changes of the topological structure in the state space of autonomous quantum system due to the nonlinear resonance are displayed numerically with the uncertainty measure of a special initial state and the transformation matrix . The statistical behavior of the subspace occupied by the state in eigenspace of quantum nonintegrable system is discussed carefully with the help of a special renormalization method. The results show that the randomness of effective Hamiltonian matrix, the transition matrix and the nearest level spacings in this region can be described by random matrix theory. And the extent of agreement of our calculation with the prediction of GOE is in correspondence to the extent of the classical torus violation.