The static conductivity of disordered systems at zero temperature and the localization of states

The static conductivity of a disordered system at T = 0 is calculated by means of a gauge-invariant approach proposed by us earlier.We obtain localization of eigenstates in a strict sense, i.e. in the sense of vanishing of the conductivity, both in 1-D systems where an exponential vanishing with the length of the chain follows and in 3-D systems where localized states are shown to correspond to the vanishing of the imaginary part of the self-energy.