Colored noise in the fractional quantum Hall effect: Duality relations andexact results

We study noise in the problem of tunneling between fractional quantum Hall edge states within a four-probe geometry. We explore the implications of th e strong-weak coupling duality symmetry existent in this problem for relati ng the various density-density autocorrelations and cross correlations betw een the four terminals. We identify correlations that transform as either " odd" or "antisymmetric," or "even" or "symmetric" quantities under duality. We show that the low-frequency noise is colored and that the deviations fr om white noise are exactly related to the differential conductance. We show explicitly that the relationship between the slope of the low-frequency no ise spectrum and the differential conductance follows from an identity that holds to all orders in perturbation theory, supporting the results implied by the duality symmetry. This generalizes the results of quantum suppressi on of the finite frequency noise spectrum to Luttinger liquids and fraction al statistics quasiparticles. [S0163-1829(99)07227-6].