  We compare the conductance of an interacting ring of six lattice sites
threaded by flux $\pi$ in a two terminal setup with the conductance of the
corresponding Kohn-Sham particles. Based on symmetry considerations we can show
that even within (lattice) Density Functional Theory employing the exact
Functional the conductance of the Kohn-Sham particles is exactly zero, while
the conductance of the physical system is close to the unitary limit. We show
that this fundamental problem might be solved by extending the standard DFT
scheme.
