Quantum dynamics of ultrasmall tunnel junctions: Real-time analysis

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Abstract
We present a real-time path-integral analysis of the quantum dynamics of an ultrasmall tunnel junction interacting with an arbitrary external impedance. For a normal junction, we derive a quasiclassical Langevin equation for the phase variable and calculate the I-V curve beyond perturbation theory for the junction conductance. In the superconducting case, we develop a nonperturbative calculation of the time-dependent expectation value of the voltage operator and voltage-voltage correlation functions. Provided that dissipation is small enough, both of these quantities show damped oscillations and a power-law decay in the low-temperature limit. We also analyze the effect of resonant voltage steps on the I-V curve of an ac-driven tunnel junction and evaluate the linewidth of Bloch oscillations in the quantum limit.