Spectral fluctuations in the three-level LMG model

Spectra of time reversal invariant system whose classical analogs are K systems show the same fluctuation properties as predicted by GOE. This hypothesis of Bohigas, Giannoni, and Schmidt is supported by numerical studies of spectral fluctuations for several Hamiltonians that describe particles in a potential well: Sinai's billiard, the stadium billiard, and the two-dimensional harmonic oscillator perturbed by fourth and sixth order terms. The authors' work extends these studies to the three-level Lipkin-Meshkov-Glick model (LMG), an essentially quantum Hamiltonian mimicking a nuclear shell model