Electron localisation in 1D-the general case

1D systems have proved amenable to both numerical and analytical calculation. Previous work has shown how to construct a theory of averaged quantities in a 1D disordered system for the case of diagonal disorder. In this paper the authors extend the theory to include the case of mixed off-diagonal and diagonal disorder. An explicit expression for the inverse localisation length and density of states is evaluated for several types of disorder including mixed and off-diagonal disorder. In addition they obtain the relations for the localisation length: l approximately=E - nu as E to 0 and l approximately=W -s for pure off-diagonal disorder. Their results are compared with published simulations and are found to be in good agreement.