Self-consistent theory of localization within site and wave approaches

The mutual complementarity of the Anderson site representation and the Edwards wave approach is considered within the frame work of the quantum-statistical theory. The former is used for the description of one-particle excitations. Based on the permutational symmetry analysis of the wave function, it is shown that the symmetry of the Anderson Hamiltonian exceeds that of the space of states. Transition to an extended state is represented within the framework of the quasi-averages theory as a phase transition of order 2+δ , where δ → 0 is an addition caused by the appearance of a logarithm. A study of the collective mode is possible within the framework of the Edwards wave representation. The examination is reduced to determining the charge distribution autocorrelation function which is expressed in terms of higher correlators of current density and generalised force, using the Mori technique. Dependences of the conductivity and polarizability on the level spread width and Fermi energy are determined. The form of the frequency dependence of the conductivity as well as the spatial dispersion pattern are analyzed.