Current oscillations in a metallic ring threaded by a time-dependent magnetic flux

We study a mesoscopic metallic ring threaded by a magnetic flux which varies linearly in time Phi(M)(t)=Phit with a formalism based in Baym-Kadanoff-Keldysh nonequilibrium Green functions. We propose a method to calculate the Green functions in real space and we consider an experimental setup to investigate the dynamics of the ring by recourse to a transport experiment. This consists of a single lead connecting the ring to a particle reservoir. We show that different dynamical regimes are attained depending on the ratio hPhi/Phi(0)W, with Phi(0)=hc/e and W the bandwidth of the ring. For moderate lengths of the ring, a stationary regime is achieved for hPhi/Phi(0)>W. In the opposite case with hPhi/Phi(0)less than or equal toW, the effect of Bloch oscillations driven by the induced electric field manifests itself in the transport properties of the system. In particular, we show that in this time-dependent regime a tunneling current oscillating in time with a period tau=2piPhi(0)/Phi can be measured in the lead. We also analyze the resistive effect introduced by inelastic scattering due to the coupling to the external reservoir.