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Time-dependent Transport in arbitrary extended driven tunnel junctions

We develop a very general perturbative theory of time-dependent transport in a weak tunneling junction which is independent of experimental details and on many-body correlated states in the coupled conductors. These can be similar or different, with arbitrary internal or mutual interactions, superconducting correlations, disorder, and coupled to an electromagnetic environment or other quantum systems. The junction can be spatially extended, and is subject, simultaneously, to time-dependent voltage, local magnetic field and modulation of the tunneling amplitudes. All observables at arbitrary frequencies: average current, non-equilibrium admittance and current correlations can be expressed in a universal way through the out-of-equilibrium DC current only, yielding perturbative time-dependent non-equilibrium fluctuation relations. In particular, charge fluctuations are shown to be universally super-poissonian, and to become poissonian if the junction is driven by a series of Lorentzian pulses. We also generalize, for constant voltage and tunneling, the poissonian shot noise and the fluctuation relation between the derivatives of the noise and the conductance. Thus we provide a compact, general and transparent unifying theory at arbitrary dimension, in contrast with involved derivations based explicitly on particular models and profiles of a single time-varying field.