Klein factors in multiple fractional qua

A fractional quantum Hall liquid with multiple edges is considered in this study. The objective is to compute transport quantities such as current, noise, and noise cross correlations in multiple edge samples, requiring the implementation of Klein factors to ensure correct quasiparticle exchange properties. Using a non-equilibrium Green's function formalism, the commutation relations of these Klein factors are derived for a simple Laughlin fraction of the Hall effect. The study explicitly demonstrates the role of Klein factors in calculating the noise cross correlations and addresses the corrections to the Poisson limit for the noise. Although previous research has focused more on systems with single edges, this paper emphasizes the importance of exploring multi-edge geometries and their unique characteristics in relation to quasiparticles statistics. The findings indicate that the detection of noise correlations in systems with three edges can yield significant insights regarding quasiparticle behavior and interactions. This work aims to provide a pedagogical view of how fractional statistics and their associated tunneling phenomena are modulated by Klein factors in complex fractional Hall setups.