Conductance of nanosystems with interaction

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The zero-temperature linear response conductance through an interacting mesoscopic region attached to noninteracting leads is investigated. We present a set of formulas expressing the conductance in terms of the ground-state energy of an auxiliary system, namely a ring threaded by a magnetic flux and containing the correlated electron region. We prove that the formalism is exact if the ground state of the system is a Fermi liquid. We show that in such systems the ground-state energy is a universal function of the magnetic flux, where the conductance is the relevant parameter. The method is illustrated with results for the transport through an interacting quantum dot and a simple Aharonov-Bohm ring with Kondo-Fano resonance physics.