We present a theoretical framework for the statistics of low-frequency current and voltage fluctuations of a quantum conductor embedded in a linear electromagnetic environment. It takes the form of a Keldysh field theory with a generic low-frequency limit that allows for a phenomenological understanding and efficient evaluation of the statistics in the saddle-point approximation. This provides an adequate theoretical justification of our earlier calculation that made use of the so-called “cascaded Langevin approach.” We show how a feedback from the environment mixes correlators of different orders. This explains the unexpected temperature dependence of the third moment of tunneling noise observed in a recent experiment. At finite temperature, current and voltage correlators of order 3 and higher are no longer linearly related. We show that a Hall bar measures voltage correlators in the longitudinal voltage and current correlators in the Hall voltage. Next, we demonstrate that the quantum high-frequency corrections to the low-frequency limit correspond to the environmental Coulomb blockade. We prove that the leading order Coulomb blockade correction to the $n\mathrm{th}$ cumulant of the current fluctuations is proportional to the voltage derivative of the $\mathrm{}(n+1\mathrm{})\mathrm{}-\mathrm{t}\mathrm{h}$ cumulant. This generalizes to any n earlier results obtained for $n=1,2.\mathrm{}$

• Received 16 June 2003

DOI:https://doi.org/10.1103/PhysRevB.69.035336