Point contact tunneling in the fractional quantum Hall effect: an exact determination of the statistical fluctuations

In the weak backscattering limit, point contact tunneling between quantum Hall edges is well described by a Poissonian process where Laughlin quasiparticles tunnel independently, leading to the unambiguous measurement of their fractional charges. In the strong backscattering limit, the tunneling is well described by a Poissonian process again, but this time involving real electrons. In between, interactions create essential correlations, which we untangle exactly in this Letter. Our main result is an exact closed form expression for the probability distribution of the charge $N(t)$ that tunnels in the time interval $t$. Formally, this distribution corresponds to a sum of independent Poisson processes carrying charge $\nu e$, $2\nu e$, etc., or, after resummation, processes carrying charge $e$, $2e$, etc. In the course of the proof, we compare the integrable and Keldysh approaches, and find, as a result of spectacular cancellations between perturbative integrals, the expected agreement.