  The authors report magnetic measurements of fluxoid transitions in
mesoscopic, superconducting aluminum rings. The transitions are induced by
applying a flux to the ring so that the induced supercurrent approaches the
critical current. In a temperature range near $T_c$, only a single fluxoid
enters or leaves at a time, leading to a final state above the ground state.
Upon lowering the temperature, several fluxoids enter or leave at once, and the
final state approaches the ground state, which can be reached below
approximately 0.5 $T_c$. A model based on the widely used time dependent
Ginzburg-Landau theory for gapless superconductors can only explain the data if
unphysical parameters are used. Heating and quasiparticle diffusion may be
important for a quantitative understanding of this experiment, which could
provide a model system for studying the nonlinear dynamics of superconductors
far from equilibrium.
