  As a consequence of the Aharonov-Bohm effect, there is a quantum-induced
attraction between a charged particle and a rigid, impenetrable hoop made from
an arbitrarily thin tube containing a superconductor quantum of magnetic flux.
This is remarkable because in classical physics there is no force between the
two objects, and quantum-mechanical effects (associated with uncertainty
principle energy) generally are repulsive rather than attractive. For an
incident spinless charged particle in a P wave (in a configuration with total
angular momentum zero) we verify a resonance just above threshold using the
Kohn variational principle in its S-matrix form. Even if optimistic choices of
parameters describing a model system with these properties turned out to be
feasible, the temperature required to observe the resonance would be far lower
than has yet been attained in the laboratory.
