Average persistent current in a mesoscopic ring

We present a microscopic calculation of the disorder-averaged persistent current for a mesoscopic ring with a fixed number of electrons. Using an idea by Imry, we show that the even Fourier components of the average current dominate and are related to the typical single-lvel current 〈${\mathit{I}}_{2\mathit{p}}$ ${\mathrm{〉}}_{\mathit{D}}$∝〈${\mathit{i}}_{\mathit{p}}^2$ ${\mathrm{〉}}_{\mathit{D}}$/${\mathit{I}}_0$, which can be calculated by a Green’s-function averaging technique. For the small, even harmonics p, the result simplifies to 〈${\mathit{I}}_{2\mathit{p}}$ ${\mathrm{〉}}_{\mathit{D}}$≊${\mathit{I}}_0$/2πM, where M is the number of transverse channels. Its relevance to multiring experiments is discussed.