Persistent differences between canonical and grand canonical averages in mesoscopic ensembles: Large paramagnetic orbital susceptibilities

Disorder-averaged thermodynamic quantities within the canonical ensemble are expressed in terms of fluctuations in the grand canonical ensemble, and are then evaluated for the diffusive regime. The particular example of persistent currents in Aharanov-Bohm geometries is addressed, and the harmonics of the disorder-averaged current (which is 1/2${\mathrm{\Phi }}_0$ periodic) are obtained. The orbital susceptibility of a mesoscopic system, disorder averaged over the canonical ensemble, may be large and positive, even for systems which, on a larger scale, should exhibit Landau diamagnetism.