  Standard concepts of nuclear physics explaining the systematics of ground
state spins in nuclei by the presence of specific coherent terms in the
nucleon-nucleon interaction were put in doubt by the observation that these
systematics can be reproduced with high probability by randomly chosen
rotationally invariant interactions. We review the recent development in this
area, along with new original results of the authors. The self-organizing role
of geometry in a finite mesoscopic system explains the main observed features
in terms of the created mean field and correlations that are considered in
analogy to the random phase approximation.
