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Perturbative fluctuation dissipation relation for non-equilibrium finite frequency noise in quantum circuits

We develop a general perturbative computation of finite-frequency quantum noise which applies, in particular, to both good or weakly transmitting strongly correlated conductors coupled to a generic environment. Under a minimal set of hypotheses, we show that the noise can be expressed through the non-equilibrium DC current only, generalizing a non-equilibrium fluctuation dissipation relation. We use this relation to derive explicit predictions for the non equilibrium finite frequency noise for a single channel conductor connected to an arbitrary Ohmic environment.