David Logan

Abstract:

We consider a disordered Hubbard model for a system characterized by quenched liquid-like disorder, with correlation treated at the generalized Hartree-Fock level and the possibility of local magnetic moments introduced from the outset. A simple theory based on averaged Green functions is used to describe the properties of the system in the local moment domains in particular, and their evolution with number density and both structural and electronic parameters of relevance. A probabilistically based mean-field theory is then developed to ' address the localization characteristics of the HF pseudoparticle states, and the consequent disorder-induced metal-insulator transition. Three principal density domains of interest are identified: a low density insulator with local magnetic moments, a metallic phase with local moments at intermediate densities, and a higher density nonmagnetic metallic state. The theory is used to provide an interpretation of bulk experiments on expanded fluid alkali elements, with particular emphasis on the insulating and "dirty" metallic domains. © 1991 American Institute of Physics.

Abstract:

A theory is developed to describe the electronic densities of states and localization characteristics of a multiband tight-binding model for a system characterized by quenched liquid-like disorder. For the case of an sp 3 system, and with parameters appropriate to fluid mercury at an independent electron level of description, the role of localization is found to be important: localized Fermi-level states persist up to densities considerably higher than that at which the s-p band gap closes. © 1990 American Institute of Physics.

Abstract:

The quantum mechanics of energy flow in many-dimensional Fermi resonant systems has several connections to the theory of Anderson localization in disordered solids. We argue that in high dimensional and highly quantum mechanical systems the energy flow can be modeled as coherent transport on a locally but weakly correlated random energy surface. This model exhibits a sharp but continuous transition from local to global energy flow characterized by critical exponents. Dephasing smears the transition and an interesting nonmonotonic dependence of energy flow rate on environmental coupling is predicted to occur near the transition. © 1990 American Institute of Physics.

Abstract:

From an exact theory presented in a previous paper (see Logan and Winn, 1988), the authors develop systematically an approximate single-site description for the density of states of a random tight-binding model characterised by quenched liquid-like disorder. The resultant theory is formally equivalent to the single super-chain approximation (SSCA) introduced by Wertheim (1973) in the context of classical dielectric theory. The authors show that the SSCA is equivalent to the effective-medium approximation (EMA) of Roth (1976), and further, for a simple choice of the pair distribution function, that the SSCA/EMA is formally equivalent to the mean spherical approximation of liquid-state theory. For a Yukawa transfer matrix element, an analytic solution of the SSCA/EMA is derived and its predictions discussed. A comparison is also made with the Matsubara-Toyozawa approximation (1961) to illustrate the effect of including the structural characteristics of the system. Finally, the authors discuss some straightforward extensions of the theory including incorporation of site-diagonal disorder, multiple-hopping processes, and the effects of orbital overlap.