  We analyze dephasing by electron interactions in a small disordered quasi-one
dimensional (1D) ring weakly coupled to leads, where we recently predicted a
crossover for the dephasing time $\tPh(T)$ from diffusive or ergodic 1D
($\tPh^{-1} \propto T^{2/3}, T^{1}$) to $0D$ behavior ($\tPh^{-1} \propto
T^{2}$) as $T$ drops below the Thouless energy $\ETh$. We provide a detailed
derivation of our results, based on an influence functional for quantum Nyquist
noise, and calculate all leading and subleading terms of the dephasing time in
the three regimes. Explicitly taking into account the Pauli blocking of the
Fermi sea in the metal allows us to describe the $0D$ regime on equal footing
as the others. The crossover to $0D$, predicted by Sivan, Imry and Aronov for
3D systems, has so far eluded experimental observation. We will show that for
$T \ll \ETh$, $0D$ dephasing governs not only the $T$-dependence for the smooth
part of the magnetoconductivity but also for the amplitude of the
Altshuler-Aronov-Spivak oscillations, which result only from electron paths
winding around the ring. This observation can be exploited to filter out and
eliminate contributions to dephasing from trajectories which do not wind around
the ring, which may tend to mask the $T^{2}$ behavior. Thus, the ring geometry
holds promise of finally observing the crossover to $0D$ experimentally.
