A SIMPLE INTERPRETATION OF ELECTRON LOCALISATION BEHAVIOUR IN WEAKLY DISORDERED SYSTEMS

Abstract
A simple relation between the local energy spectrum and the time evolution of a wavepacket diffusing in a disordered system is discussed. In conjunction with Polya's theorem for random walks, this relation implies an electron local density of states which in one and two dimensions is not square integrable over energy. Such a local density of states is infinitely spiky however weak the disorder. It is suggested that this effect is a symptom of the localised electron eigenstates which always exist in one and two dimensional disordered systems according to recent theories. By considering the smoothing of the local density of states as a function of inelastic scattering time one can deduce a time scale beyond which conventional weak-scattering transport theory breaks down. Assuming this breakdown is a manifestation of localisation one can obtain estimates of the localisation length. These agree with well established results for one dimension and the more recent scaling type of result for two dimensions.