  We use the Lanczos method to calculate the variance of the number of energy
levels in an energy window of width E below the Fermi energy for
non-interacting disordered electrons on a thin three-dimensional ring threaded
by an Aharonov-Bohm flux . We find that for small E the flux-dependent part of
the variance is well described by a well-known Feynman diagram involving two
Cooperons. However, this result cannot be extrapolated to energies E where the
energy-dependence of the average density of states becomes significant. We
discuss consequences for persistent currents.
