  We study dephasing by electron interactions in a small disordered quasi-one
dimensional (1D) ring weakly coupled to leads. We use an influence functional
for quantum Nyquist noise to describe the 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. The crossover to 0D, predicted earlier for 2D and 3D systems, has so
far eluded experimental observation. The ring geometry holds promise of meeting
this longstanding challenge, since the crossover manifests itself not only in
the smooth part of the magnetoconductivity but also in the amplitude of
Altshuler-Aronov-Spivak oscillations. This allows signatures of dephasing in
the ring to be cleanly extracted by filtering out those of the leads.
