Order out of chaos in the shell model

Nuclei at low excitation energy exhibit such well-ordered behavior, such as rotational and vibrational bands as well as pairing gaps, that they are commonly described with algebraic models; but does such order originate in the details of the nuclear force, or are they emergent properties of dense fermion systems? To answer this, I consider ensembles of random two-body shell-model interactions and examine the low-lying spectra and wavefunctions. Some striking regularities emerge: in particular, pairing appears to be a ubiquitous phenomenon, even in the absence of explicit pairing interactions! These results are remarkably insensitive to the detailed definition of the ensemble.