Direct link between Coulomb blockade and shot noise in a quantum-coherent structure

We analyze the current-voltage characteristic of a quantum conduction channel coupled to an electromagnetic environment with arbitrary frequency-dependent impedance. In the weak blockade regime the correction to the Ohmic behavior is directly I elated to the channel current fluctuations, vanishing at perfect transmission in the same way as shot noise. This relation can be generalized to describe the environmental Coulomb blockade in a generic mesoscopic conductor coupled to an external impedance, as the response of the latter to the current fluctuations in the former.