Stochasticity of the effective subspace taken up by a coherent state in quantum system corresponding to classical chaotic one

It is well known that all torus are-destroyed in the Poincare' section with a certain energy E-0 when a classical system is in completely chaotic stat e. But in its quantum counterpart, the features of the subspace taken up by a coherent state with central energy (E) over bar(0) = E-0 is not yet clea r. In the present paper, taking nuclear Lipkin model as an example, we stud y the properties of such a subspace taken up by the coherent state of SU(3) group. An effective subspace is obtained by using a new renormalization ap proach. Our results show that in such an effective subspace the distributio n of the nearest level spacings, the elements of effective Hamiltonian matr ix, and the one-to-one correspondent map from the subspace of an integrable system to that of nonintegrable one are all consistent with predictions of random matrix theory.