Theory of a Fermi glass

We construct a theory for localized electrons in disordered solids similar in spirit and intent to the Fermiliquid theory of Landau. That is, for low temperatures and excitation energies small compared to the Fermi energy, the electrons may be viewed as forming a gas of localized quasiparticles. The phenomenological theory is presented and applications are made to both equilibrium and time-dependent properties of the glass. A microscopic justification of the quasiparticle picture is made by an examination of the single-particle Green's function of the interacting system. The collective properties of the glass are examined by studing the Bethe-Salpeter equation satisfied by the four-point vertex for particle-hole scattering. This leads to the identification of the phenomenological effective interaction between quasiparticles with a certain limit of the four-point vertex and to a microscopic justification of the phenomenological transport equation used to study time-dependent phenomena.