Cross-correlation of two interacting conductors

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 Buttiker [Phys. Rev. Lett. 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.