Aspects of Localisation in Off-Diagonally Disordered Systems.

Available from UMI in association with The British Library. Requires signed TDF. The method of numerical finite-size scaling implemented on strips and bars is extended to the case of off-diagonal disorder. Systems where the diagonal and off-diagonal matrix elements of the Hamiltonian were correlated with a Goldstone symmetry, and also where only the off-diagonal elements were random, were studied. The one-parameter scaling theory of localisation is confirmed for these systems with some idea of the limits of its validity, and this leads to a determination of the critical behaviour for the localisation length for a variety of energies, and of the critical disorder of the Anderson transition. The results thus obtained are consistent with other estimates on diagonally disordered systems, and in particular no transition is found in two dimensions. Results for the mobility edge, given by an extension of this method into the full energy-disorder plane are also presented. Using scaling assumptions and the behaviour of the density of states, many features of the observed behaviour can be at least qualitatively explained. All of these investigations are improved by a correction to scaling analysis which removes many of the systematic errors in the simple finite-size scaling approach. For comparison, a method which combines the coherent potential approximation with an equivalence between potential wells and localised systems is used to calculate the mean free path 1, and ultimately extract the localisation length and mobility edge. The shortcomings of this method for off-diagonal systems are also discussed. The conductivity obtained using both finite-size scaling and potential well methods are also presented, and the results discussed along with a brief review of the current state of experiments on localisation.