  The conductance of one-dimensional nano-wires of interacting electrons
connected to non-interacting leads is calculated in the linear response regime.
Two different approaches are used: a many-body Green function technique and a
relation to the persistent current recently proposed based on results of the
non-interacting case. The conductance is evaluated using the functional
renormalization group method and the density matrix renormalization group
algorithm. Our results give a strong indication that the idea of obtaining the
conductance from the persistent current holds for interacting systems.
