Cross-correlation of two interacting conductors

TL;DR

This paper calculates the zero-frequency current cross-correlation between two weakly interacting mesoscopic conductors, incorporating the Fermi sea and using Random Matrix Theory to analyze fluctuations in chaotic quantum dots.

Contribution

It extends previous two-particle scattering matrix approaches by including the Fermi sea and applies Random Matrix Theory to analyze current cross-correlations in chaotic quantum dots.

Findings

Calculated the magnitude of cross-correlation fluctuations.

Included the Fermi sea in the theoretical framework.

Analyzed chaotic quantum dots using Random Matrix Theory.

Abstract

We calculate the current cross-correlation for two weakly interacting mesoscopic conductors. Our derivation is based on the two-particle scattering matrix derived in Goorden and B\"uttiker [Phys. Rev. Lett. {\bf 99}, 146801 (2007)]. We include the Fermi sea in the leads into the theory and show how to calculate transport quantities and specifically cross-correlations. We focus on the zero-frequency current cross-correlation of two chaotic quantum dots and calculate the magnitude of its fluctuations with the help of Random Matrix Theory.