Analytic structure of one-dimensional localization theory: Re-examining Mott's law

It is argued that the behavior of two-particle correlation functions for a one-dimensional system of disordered electrons is not only governed by the localization length, l, but also involves a dynamical characteristic length, l ln(1/omega). This is shown to be consistent with spectral properties of the underlying Heun-type operator. One consequence of this fact is that the Mott law for the low-frequency electrical conductivity should be amended to Re sigma(omega) similar to omega(2) ln(3)(1/omega).