  We investigate the static and dynamical behavior of 1D interacting fermions
in disordered Hubbard chains, contacted to semi-infinite leads. The chains are
described via the repulsive Anderson-Hubbard Hamiltonian, using static and
time-dependent lattice density-functional theory. The dynamical behavior of our
quantum transport system is performed via an integration scheme available in
the literature, which we modify via the recursive Lanczos method, to increase
its efficiency. To quantify the degree of localization due to disorder and
interactions, we adapt the definition of the inverse participation ratio to
obtain an indicator which is both suitable for quantum transport geometries and
which can be obtained within density-functional theory. Lattice density
functional theories are reviewed and, for contacted chains, we analyze the
merits and limits of the coherent-potential approximation in describing the
spectral properties, with interactions included via lattice density functional
theory. Our approach appears to able to capture complex features due to the
competition between disorder and interactions. Specifically, we find a
dynamical enhancement of delocalization in presence of a finite bias, and an
increase of the steady-state current induced by inter-particle interactions.
This behavior is corroborated by results for the time-dependent densities and
for the inverse participation ratio. Using short isolated chains with
interaction and disorder, a brief comparative analysis between time-dependent
density-functional theory and exact results is then given, followed by general
conclusive remarks.
