Computer simulations of localization and quantum transport in a three-dimensional topologically disordered system

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Abstract
The results of simulation studies of the localization and quantum-transport characteristics of a three-dimensional, off-diagonally disordered tight-binding model are reported. The disorder is characteristic of a hard-sphere fluid, with an exponential transfer-matrix element. The properties calculated include the density of states, the band-edge and mobility-edge trajectories, and the time dependence of the averaged probability, P¯(t), that an excitation will be found at the site at which it was initially located. Localization of eigenstates is inferred from a criterion based on a cutoff in the inverse participation ratio, and an attempt is made to provide a reasoned estimate for the chosen cutoff via time-dependent studies of P¯(t). Pronounced screening effects on the band-edge and mobility-edge trajectories are found and their physical origin is discussed. The consequences of varying the ratio of the hard-sphere diameter to the range of the exponential interaction are investigated. The results obtained for the hard-sphere fluid are contrasted with those for a randomly substituted lattice at the same density.