Yz. Xing et Go. Xu, Stochasticity of the effective subspace taken up by a coherent state in quantum system corresponding to classical chaotic one, ACT PHY C E, 48(5), 1999, pp. 769-774
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.