Linear Transport within the Kubo Formalism

Kubo’s linear response theory is a powerful method to evaluate non-equilibrium properties of a system subject to a weak perturbation. The key idea is that, if the perturbation is weak, non-equilibrium averages of a generic observable can be obtained from equilibrium correlation functions involving the observable of interest and the perturbation Hamiltonian. Here we apply the Kubo formalism to obtain an exact formula for the conductance of interacting nanojunctions. It is expressed in terms of the current response function of the nanojunction. This quantity is in general not accessible in analytic form. Matters simplify in the case of noninteracting nanojunctions, as we show on the example of archetypal N-site systems.