Mean-field studies of embedded interacting systems out of equilibrium

We provide an analytical expression to calculate the conductance of a system-bath setup at finite temperatures for non-interacting systems. This serves as an extension to the famed Greenwood-Kubo formula used to calculate the conductance of non-interacting systems at zero temperature. This is possible due to the introduction of the concept of "embedding" to mimic a system connected to semi-infinite baths at its ends. Along with the conductance, we also provide analytical expressions for the onsite occupation at zero and finite temperatures. As an application, we study the effect of interaction on the localization properties of the 1D Anderson chain at zero temperature. The interaction used is repulsive Hubbard type, calculated at the mean field level self consistently. Both occupation and conductance clearly show that even at the mean field level, interaction brings in delocalization in this system. The interaction induced correlation among the onsite potentials is further studied. Finally, the concept of localization landscape is used to analyse localization trends seen in our self-consistent Hamiltonians.