  The major finding of this paper is that a one-dimensional spin-polarized gas
comprised of an even number of fermionic atoms interacting via attractive
p-wave interactions and confined to a mesoscopic ring has a degenerate pair of
ground states that are oppositely rotating. In any realization the gas will
thus spontaneously rotate one way or the other in spite of the fact that there
is no external rotation or bias fields. Our goal is to show that this
counter-intuitive finding is a natural consequence of the combined effects of
quantum statistics, ring topology, and exchange interactions.
