Bloch-like oscillations induced by charge discreteness in quantum mesoscopic rings

We study the effect of charge discreteness in a quantum mesoscopic ring wih inductance L. The ring is pierced by a time depending external magnetic field. When the external magnetic flux varies uniformly, the current induced in the ring oscillates with a frequency proportional to the charge discreteness and the flux variation. This phenomenon is very similar to the well known Bloch's oscillation in crystals. The similitude is related to the charge discreteness in the charge-current representation, which plays the same role as the constant lattice in crystals.