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We study the amplitude of mesoscopic Aharonov-Bohm oscillations inquasi-one-dimensional (Q1D) diffusive rings. We consider first thelow-temperature limit of a fully coherent sample. The variance of oscillationharmonics is calculated as a function of the length of the leads attaching thering to reservoirs. We further analyze the regime of relatively hightemperatures, when the dephasing due to electron-electron interactionsuppresses substantially the oscillations. We show that the dephasing lengthL_phi^AB governing the damping factor exp(-2pi R /L_phi^AB) of the oscillationsis parametrically different from the common dephasing length for the Q1Dgeometry. This is due to the fact that the dephasing is governed by energytransfers determined by the ring circumference 2pi R, making L_phi^ABR-dependent.Comment: 16 pages, 4 figures, to appear in proceedings of NATO/Euresco  Conference "Fundamental Problems of Mesoscopic Physics: Interactions and  Decoherence", Granada (Spain), September 200

Mesoscopic Aharonov-Bohm Oscillations in Metallic Rings