Colored noise in the fractional Hall effect: duality relations and exact results

TL;DR

This paper investigates noise characteristics in fractional quantum Hall edge state tunneling, revealing duality relations and exact connections between low-frequency noise, differential conductance, and quantum statistics.

Contribution

It demonstrates the exact relationship between noise deviations and conductance in fractional quantum Hall systems, generalizing previous results to Luttinger liquids and quasiparticles.

Findings

Low frequency noise is colored with deviations related to conductance.

Duality symmetry links auto- and cross-correlations in the system.

The noise-conductance relationship holds to all orders in perturbation theory.

Abstract

We study noise in the problem of tunneling between fractional quantum Hall edge states within a four probe geometry. We explore the implications of the strong-weak coupling duality symmetry existent in this problem for relating the various density-density auto-correlations and cross-correlations between the four terminals. We identify correlations that transform as either ``odd'' or ``anti-symmetric'', or ``even'' or ``symmetric'' quantities under duality. We show that the low frequency noise is colored, and that the deviations from white noise are exactly related to the differential conductance. We show explicitly that the relationship between the slope of the low frequency noise spectrum and the differential conductance follows from an identity that holds to {\it all} orders in perturbation theory, supporting the results implied by the duality symmetry. This generalizes the results of quantum supression of the finite frequency noise spectrum to Luttinger liquids and fractional statistics quasiparticles.