  We study a method to determine the residual conductance of a correlated
system by means of the ground-state properties of a large ring composed of the
system itself and a long non-interacting lead. The transmission probability
through the interacting region and thus its residual conductance is deduced
from the persistent current induced by a flux threading the ring. Density
Matrix Renormalization Group techniques are employed to obtain numerical
results for one-dimensional systems of interacting spinless fermions. As the
flux dependence of the persistent current for such a system demonstrates, the
interacting system coupled to an infinite non-interacting lead behaves as a
non-interacting scatterer, but with an interaction dependent elastic
transmission coefficient. The scaling to large lead sizes is discussed in
detail as it constitutes a crucial step in determining the conductance.
Furthermore, the method, which so far had been used at half filling, is
extended to arbitrary filling and also applied to disordered interacting
systems, where it is found that repulsive interaction can favor transport.
