Electron dynamics and Anderson localization in Wigner formulation of quantum statistical mechanics

The new numerical approach for consideration of quantum dynamics and calcul ations of the average values of quantum operators and time correlation func tions in the Wigner representation of quantum statistical mechanics has bee n developed. The time correlation functions have been presented in the form of the integral of the Weyl's symbol of considered operators and the Fouri er transform of the product of matrix elements of the dynamic propagators. For electrons in disordered systems of scatterers the numerical results hav e been obtained for series of the average values of the quantum operators i ncluding position and momentum dispersions, average energy, energy distribu tion function as well as for the frequency dependencies of tensor of electr on conductivity and permittivity according to quantum Kubo formula. Zero or very small value of static conductivity have been considered as the manife station of Anderson localization of electrons in 1D case.