Periodicity of the Aharonov-Bohm effect in normal-metal rings

We study the Aharonov-Bohm effect in single normal-metal rings and show that averaging the conductance over many energies is equivalent to ensemble averaging. Thus raising the temperature T above a crossover ${\mathrm{T}}_{\mathrm{c}}$ changes the flux periodicity of magnetoresistance oscillations from h/e to h/2e. ${\mathrm{T}}_{\mathrm{c}}$ is determined by an energy correlation range, hD/${\mathrm{L}}^2$. The persistence of the h/e oscillations to high fields is explained.