Dimensional crossover of the dephasing time in disordered mesoscopic rings

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 tau(phi)(T) from diffusive or ergodic 1D (tau(-1)(phi)alpha T-2/3,T-1) to zero-dimensional (0D) behavior (tau(-1)(phi)alpha T-2) as T drops below the Thouless energy. The crossover to 0D, predicted earlier for two-dimensional and three-dimensional systems, has so far eluded experimental observation. The ring geometry holds promise of meeting this long-standing 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.