  Low-lying collective states involving many nucleons interacting by a random
ensemble of two-body interactions (TBRE) are investigated in a collective
SD-pair subspace, with the collective pairs defined dynamically from the
two-nucleon system. It is found that in this truncated pair subspace collective
vibrations arise naturally for a general TBRE hamiltonian whereas collective
rotations do not. A hamiltonian restricted to include only a few randomly
generated separable terms is able to produce collective rotational behavior, as
long as it includes a reasonably strong quadrupole-quadrupole component.
Similar results arise in the full shell model space. These results suggest that
the structure of the hamiltonian is key to producing generic collective
rotation.
