Abstract
The transition to chaos as the development of global nonintegrability in a three-level Lipkin model is investigated numerically. With effective Hamiltonians for different energy regions it is possible to study local statistical behaviors of the system in the corresponding energy regions. Behaviors of its classical counterparts are also given for comparison. The dynamical origin of statistical properties of effective Hamiltonian matrices is qualitatively explained. The question of what are the members of the Gaussian orthogonal ensemble is also discussed.
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