  We study Density Functional Theory models for systems which are
transitionally invariant in some directions, such as a homogeneous 2-d slab in
the 3-d space. We show how the different terms of the energy are modified and
we derive reduced equations in the remaining directions. In the Thomas-Fermi
model, we prove that there is perfect screening, and provide precise decay
estimates for the electronic density away from the slab. In Kohn-Sham models,
we prove that the Pauli principle is replaced by a penalization term in the
energy. In the reduced Hartree-Fock model in particular, we prove that the
resulting model is well-posed, and provide some properties for the minimizer.
