Non-linear response and electron-electron interactions in mesoscopic metal rings

A time-dependent electric field gives rise to a stationary non-equilibrium current $I^{(2)}$ around a mesoscopic metal ring threaded by a magnetic flux. We show that this current, which is proportional to the intensity of the field, is closely related to the exchange part of the interaction contribution to the equilibrium persistent current, and that the corresponding non-linear conductivity directly measures the weak localization correction to the polarization. We explicitly calculate the disorder average of $I^{(2)}$ in the diffusive regime as function of the frequency of the electric field and the static flux piercing the ring, and suggest an experiment to test our theory