Time-dependent Transport in arbitrary extended driven tunnel junctions

We develop a very general perturbative theory of time-dependent transport in weak tunneling junctions that is independent of experimental details and applicable to many-body correlated states in coupled conductors. These systems can display both similar and different internal interactions, superconducting correlations, and disorder, while being subject to an electromagnetic environment or other quantum systems. Our analysis encompasses a spatially extended junction, influenced by simultaneous time-dependent voltage, local magnetic fields, and modulation of the tunneling amplitudes. We derive universal expressions for observables across arbitrary frequencies—including average current, non-equilibrium admittance, and current correlations—exclusively through the out-of-equilibrium DC current, leading to perturbative time-dependent non-equilibrium fluctuation relations. Notably, charge fluctuations we investigate are found to be universally super-poissonian, transitioning to poissonian characteristics under the influence of Lorentzian pulses. Additionally, we extend the understanding of poissonian shot noise and the fluctuation relation between noise derivatives and conductance for constant voltage and tunneling conditions. Our work provides a compact and transparent unifying theory applicable in arbitrary dimensions, contrasting with traditional models reliant on particular configurations and varying fields.