Fermi’s golden rule in a mesoscopic metal ring

We examine the time-dependent nonequilibrium current in a mesoscopic metal ring threaded by a static magnetic flux φ that is generated by a time-dependent electric field oscillating with frequency ω. We show that in quadratic order in the field there are three fundamentally different contributions to the current. (a) A time-independent contribution which can be obtained from a thermodynamic derivative. (b) A term increasing linearly in time that can be understood in terms of Fermi’s golden rule. The derivation of this term requires a careful treatment of the infinitesimal imaginary parts that are added to the real frequency ω when the electric field is adiabatically switched on. (c) Finally, there is also a time-dependent current oscillating with frequency 2 ω. We suggest an experiment to test our results.