SCATTERING PHASE-SHIFT ANALYSIS OF PERSISTENT CURRENTS IN MESOSCOPIC AHARONOV-BOHM GEOMETRIES

The ensemble average of the persistent currents of Aharonov-Bohm mesoscopic rings is evaluated in a case where the number of electrons rather than the chemical potential is fixed. The difference between the average currents in these two situations is expressed on general grounds in terms of the fluctuation of the scattering phase shift. It is then shown that in the diffusive regime this difference is (h/2e)-periodic and does not depend on the disorder. Possible extensions of the approach used here are emphasized.