ORDERLY SPECTRA FROM RANDOM INTERACTIONS

We investigate the low-lying spectra of many-body systems with random two-body interactions, specifying that the ensemble be invariant under particle-hole conjugation. Surprisingly we find patterns reminiscent of more orderly interactions, such as a predominance of J=0 ground states separated by a gap from the excited states, and evidence of phonon vibrations in the low-lying spectra. {copyright} {ital 1998} {ital The American Physical Society}