Decay of Persistent Currents in Small Superconductors

The thermodynamic fluctuations of the order parameter in a superconductor are shown to be able to cause the decay of a "persistent" current in a ring-shaped conductor. Calculations have been made of the lifetimes of these currents, which indicate that in very thin wires this decay should be detectable. We also show that a true phase transition, distinguished by an infinitely sharp change of resistivity, is possible only in an infinite three-dimensional specimen. In one- and two-dimensional samples, on the other hand, no infinitely sharp change of resistivity occurs but, instead, the resistance drops smoothly and rapidly towards zero as $T\to 0$°K.