Mean-field electronic structure models for disordered materials

We set up a functional setting for mean-field electronic structure models of Hartree-Fock or Kohn-Sham types for disordered quantum systems. We then use these tools to study a specific mean-field model (reduced Hartree-Fock, rHF) for a disordered crystal where the nuclei are classical particles whose positions and charges are random. We prove the existence of a minimizer of the energy per unit volume and the uniqueness of the ground state density. For (short-range) Yukawa interactions, we prove in addition that the rHF ground state density matrix satis_es a self-consistent equation, and that our model is the thermodynamic limit of the supercell model.