David Logan

Abstract:

An analysis is given for the configurationally averaged Green functions of a random multi-level tight-binding model characterised by quenched liquid-like disorder, using graph-theoretical methods. An exact self-consistency equation for the average diagonal Green function matrix, G(z), is derived, from which follow the partial densities of states (DOS). From the exact description, various approximate theories for G(z) may be developed systematically. The authors examine in particular three tractable theories for the case of a two-band system: the Hubbard approximation, the Matsubara-Toyozawa approximation and the single super-chain approximation (SSCA) which is equivalent to the effective medium approximation (EMA) of Roth (1974, 1976). With Yukawa transfer matrix elements the SSCA/EMA is solved analytically by exploiting direct analogies with the theory of classical binary liquid mixtures. For all three theories the material parameter dependence of the DOS is examined systematically and comparatively, with particular regard to band overlap effects which may lead to a metal-insulator transition.

Abstract:

An approximate but soluble single-site theory for the density of states of a two-band spatially disordered system, the single super-chain approximation/effective-medium approximation (SSCA/EMA), is compared with direct simulations on and off-diagonally disordered, two-level tight-binding model. The theory reproduces the simulations remarkably well.

Abstract:

The adequacy and range of applicability of an analytically soluble single site theory for the density of states of a spatially disordered system is assessed by comparison with numerical simulations on an off-diagonally disordered tight-binding model. The validity of a non-single site theory, appropriate in the low-density domain, is also examined by comparison with simulation.

Abstract:

A molecular theory is given for the thermodynamic state dependence of the Raman noncoincidence effect, arising from transition dipolar resonant transfer in dipolar binary liquid mixtures. Predictions of the theory are discussed, and some suggestions for possible experiments are made. © 1989.