Aharonov-bohm effect in normal-metal rings of finite width: a variational study

We use a variational method to calculate the conductance correlation function for a disordered normal-metal ring of finite width, in the mesoscopic regime $L\le L_{\phi }$. Our results show clearly the aperiodic "universal" conductance fluctuations and $\frac{\mathrm{hc}}{e}$ Aharonov-Bohm oscillations. They also provide a rough estimate for the size of the magnetic field, which causes dephasing of these effects due to its penetration of the annulus of the mesoscopic ring. We also present a simple argument, based on random-walk numerical simulations, for the experimentally observed relation between the dephasing fields for aperiodic fluctuations (AF) and the $\frac{\mathrm{hc}}{e}$ oscillations: ${\Delta H}_c^{\mathrm{AF}}\approx {2\Delta H}_c^{\frac{\mathrm{hc}}{e}}$.