Abstract
We study a mesoscopic metallic ring threaded by a magnetic flux which varies linearly in time ${\ensuremath{\Phi}}_{M}(t)=\ensuremath{\Phi}t$ 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 $\ensuremath{\Elzxh}\ensuremath{\Phi}/{\ensuremath{\Phi}}_{0}W,$ with ${\ensuremath{\Phi}}_{0}=hc/e$ and W the bandwidth of the ring. For moderate lengths of the ring, a stationary regime is achieved for $\ensuremath{\Elzxh}\ensuremath{\Phi}/{\ensuremath{\Phi}}_{0}>W.$ In the opposite case with $\ensuremath{\Elzxh}\ensuremath{\Phi}/{\ensuremath{\Phi}}_{0}<~W,$ 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 $\ensuremath{\tau}=2\ensuremath{\pi}{\ensuremath{\Phi}}_{0}/\ensuremath{\Phi}$ can be measured in the lead. We also analyze the resistive effect introduced by inelastic scattering due to the coupling to the external reservoir.
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