Non-ergodic behaviour of the k-body embedded Gaussian random ensembles for bosons

We investigate the shape of the spectrum and the spectral fluctuations of the k-body embedded Gaussian ensemble for bosons in the dense limit, where the number of bosons m --> infinity while both k, the rank of the interaction, and l, the number of single-particle states, are kept fixed. We show that the relative fluctuations of the low spectral moments do not vanish in this limit, proving that the ensemble is non-ergodic. Numerical simulations yield spectra which display a strong tendency towards picket-fence type. The wave functions also deviate from canonical random-matrix behaviour.