On the static conductivity of one-dimensional disordered systems

It is shown that if a one-dimensional disordered system is ergodie (conditions formulated below), the characteristic flmctions determining the conductivity have properties such that $\sigma(\omega)=0$ for $\omega=0$ ($\omega$ is the frequency of the external electric field). The connection between diffusion and the frequency dependence $\sigma(\omega)$ is investigated. Some questions associated with the density of energy levels in a random one-dimensional system are considered briefly.