David Logan

Abstract:

The authors consider the distribution of Madelung potentials (MP) in liquid monovalent binary alloys CxA1-x exhibiting a significant degree of charge transfer, with particular attention to the CxAu 1-x system. For canonical models of ionic liquids, and within the framework of linear theories such as the mean spherical approximation, the MP probability distributions are shown to be Gaussian and are studied in some detail. Fluctuations in the effective electronic site energies, arising from disorder in the distribution of site MPs, are shown to occur on the eV scale. The authors consider the consequences for electronic properties of this coulombic disorder, and its interplay with the effects of on-site electron correlations, with particular emphasis on the C-rich composition domain dose to stoichiometry.

Abstract:

Recently, experiments on expanded fluid mercury, and simulations of alkali metals in liquid ammonia and in molten alkali halides, have motivated interest in the possibility of a Frenkel excitonic insulator (EI) phase. In this paper, the authors discuss several aspects of a model for describing such a phase. They choose a model Hamiltonian which is the asymptotically exact low-density form for a system of atoms each possessing an sp3basis, and present two methods of analysis. The pairing theory centres on the broadening of the S to P atomic transition into exciton bands, which, as is known, may lead to the formation of a Frenkel EI phase. They analyse two corrections to the traditional exciton picture: (i) double-excitation processes, which are responsible for the van der Waals stabilization energy, are shown to halve the density predicted for the transition to an EI phase; (ii) correct incorporation of non-boson statistics for the exciton operators is argued to drive the transition from first order to second order. The authors also analyse the model Hamiltonian via a Hartree approximation, which proves to be the more tractable method, and further allows an explicit description of the EI phase itself. The validity of the Hartree approximation is justified by comparison with the pairing theory.

Abstract:

We consider a model system of three weakly coupled, weakly anharmonic oscillators, containing two near 2:1 Fermi resonances. By reduction to a system of two coupled pendula, the classical system can be understood in terms of predictable resonance zones and their intersection in phase space. This description is shown to have a natural quantum parallel, and the location and widths of the resonance zones in the corresponding quantum action space are likewise descrined. Results from numerical studies are given to support the description and illustrate the parallels between classical and quantum behaviour. © 1992.