Abstract
Results are presented of exact numerical calculations of the AC conductivity of a simple, physically useful model of a hopping system. The model consists of a finite one-dimensional lattice of sites with the carrier hopping by a phonon assisted process between states localized on the lattice sites. It is shown that the frequency dependence of a finite lattice of regularly spaced sites of equal energy is of the Debye type, with a 'relaxation time' which can be related to the transit time of a carrier along the finite chain. For a lattice of equal energy sites randomly distributed in space, the conductivity saturates at high frequency and at lower frequencies can be represented by sigma ( omega )=A omega s, where s<or approximately=1. For a regular lattice of sites with a random distribution of energy levels, similar frequency dependence is observed with the value of s changing systematically with temperature.