Exciton theory in amorphous materials

In the present paper a second quantization formalism is used to derive a general expression for the exciton hamiltonian in disordered materials. It is shown how exciton creation and annihilation operators, acting as bosons, can be introduced. The exciton hamiltonian is diagonalized by an appropriate transformation for the exciton operators. We furthermore introduced the concept of the electronic polarization due to an exciton. The polarization coefficients are calculated by a simple variational technique. An appropriate configurational average of the results is taken, in order to eliminate the position vectors of the different constituent atoms.     

Topics in the theory of amorphous materials

In this Colloquium, I describe some current frontiers in the physics of semiconducting amorphous materials and glasses, including a short, but self-contained discussion of techniques for creating computer models, among them the quench from the melt method, the Activation-Relaxation Technique, the decorate and relax method, and the experimentally constrained molecular relaxation scheme. A representative study of an interesting and important glass (amorphous GeSe₃:Ag) is provided. This material is a fast-ion conductor and a serious candidate to replace current FLASH memory. Next, I discuss the effects of topological disorder on electronic states. By computing the decay of the density matrix in real space, and also computing well-localized Wannier functions, we close with a quantitative discussion of Kohn’s Principle of Nearsightedness in amorphous silicon.     

A self-consistent cluster study of the Emery model

We calculate Fermi-surface properties of the Cuprate superconductors within the three band Hubbard model (also called the Emery model) using a cluster expansion for the proper selfenergy. The Fermi-surface topology is in agreement with angular-resolved photoemission data for dopings ～ 20%. We discuss possible violations of the Luttinger sum-rule for smaller dopings and the role of van-Hove singularities in the density of states of the Zhang-Rice singlets. We calculate the shift in the chemical potential upon doping and find quantitative agreement with recent experiments.     

A self-consistent field theory of crystals

A self-consistent theory of crystals is presented. The classical phenomenological theory of crystals is derived by means of the boson transformation method.     

A theory of vibrations of solid solutions with inclusion of the cluster effects: Non-self-consistent and self-consistent approximations

A theory of vibrational spectra of solid solutions proposed by the author has been developed, in which a cluster of n cells statistically filled with impurity atoms is used as a phonon scattering unit. The calculation of vibrational spectra of a disordered linear chain in the generalized non-self-consistent approximation has demonstrated a strong dependence of the spectrum on the number n. For n = 6, the calculated spectrum is in an excellent agreement with the result of the computer experiment performed by Dean for a chain of 8000 atoms. The maximum number of impurities in the cluster to be considered depends on the magnitude of the initial damping (in real crystals, it is damping due to anharmonicity). The spectrum has also been calculated in the generalized self-consistent approximation. This calculation gives a smeared structureless curve, which absolutely does not agree either with the theoretical calculation in the non-self-consistent approximation or with the results obtained by Dean. This means that the generalized self-consistent approximation overestimates the weight of the incoherent scattering processes, which leads to averaging of the phases. The spectrum of a three-dimensional solid solution is calculated using a simple model of the crystal.     

Quasiparticle self-consistent GW theory

In past decades the scientific community has been looking for a reliable first-principles method to predict the electronic structure of solids with high accuracy. Here we present an approach which we call the quasiparticle self-consistent approximation. It is based on a kind of self-consistent perturbation theory, where the self-consistency is constructed to minimize the perturbation. We apply it to selections from different classes of materials, including alkali metals, semiconductors, wide band gap insulators, transition metals, transition metal oxides, magnetic insulators, and rare earth compounds. Apart from some mild exceptions, the properties are very well described, particularly in weakly correlated cases. Self-consistency dramatically improves agreement with experiment, and is sometimes essential. Discrepancies with experiment are systematic, and can be explained in terms of approximations made.     

A self-consistent field scattering theory and weak asymptotic conditions

A fully self-consistent field (SCF) theory of many-particle collisions attempts to treat both the target and scattering arbitals on an equal footing, by simultaneously determining them, all self-consistently. It necessarily results in relaxation of the exact asymptotic boundary condition, because the SCF target orbitals are approximate and depend on the collision energy. Thus the original scattering problem is modified by this weak asymptotic condition (WAC) in the most fundamental was and the validity of the theory depends on multiconfiguration mixing to restore the condition. We show by extensive numerical calculations that, as more configurations are mixed, the solution converges to the correct limit. The theory is then applied to the positron-helium and electron-helium scattering systems, where the helium target functions are determined self consistently, as a part of the overall solution of the collision problem. The result shows that the weak condition is sufficient in providing physically acceptable target functions.     

On the self-consistent theory of localization

A modification of W. Götze's self-consistent approach is proposed, which predicts a complete localization in the one- and two-dimensional cases. The modification is based on a choice of such a form of the time dependence for the two-particle Green function, which takes an apparent account of time-reversal invariance.     

Drip-line nuclei in self-consistent mean-field theory

Ground state properties of exotic nuclei with extreme isospin values are discussed in the framework of self-consistent mean-field theory. The influence of particle continuum is analysed. Several effective interactions are used to investigate separation energies, radii, pairing properties, particle and pairing potentials, diproton partial decay half-lives, and shell structure of exotic nuclei.     

A self-consistent approach to quantum field theory for extended particles

A notion of quantum space-time is introduced, physically defined as the totality of all flows of quantum test particles in free fall. In quantum space-time the classical notion of deterministic inertial frames is replaced by that of stochastic frames marked by extended particles. The same particles are used both as markers of quantum space-time points as well as natural clocks, each species of quantum test particle thus providing a standard for space-time measurements. In the considered flat-space case, the fluctuations in coordinate values with respect to stochastic frames are described by coordinate probability amplitudes related to irreducible stochastic phase space representations of the Poincaré group. Lagrangian field theory on quantum space-time is formulated. The ensuing equations of motion for interacting fields contain no singularities in their nonlinear terms, and therefore can be handled by methods borrowed from classical nonlinear analysis.Supported in part by an NSERC grant.     

A neural model of hysteresis in amorphous materials and piezoelectric materials

A new approach to constructing hysteretic operator (HO) is proposed in this paper. Based on the HO, the input space of neural networks is expanded from one-dimension to two-dimension and the multi-value mapping of hysteresis is transformed into a continuous mapping comprised of one-to-one mapping and multiple-to-one mapping. Based on the expanded input space, a neural network is employed to approximate hysteresis. The results of experimental examples suggest the proposed approach is effective.     

Simple self-consistent theory of the Mott transition

A simple theory of the metal-insulator transition is proposed based on the Hubbard model of narrow-band metals.     

On the self-consistent statistical theory of vacancies

We report here a new method of describing the effect of the presence of vacancies on the structure, dynamics and thermodynamics of a crystal. The unsymmetrized self-consistent approximation is used to determine the potential energy in which the defective structure and the anharmonicity appear from the beginning. In order to stress the power of this method, we calculate the free energy of formation of a vacancy and the concentration of vacancy in a two-dimensional triangular Lennard-Jones crystal. A comparison with Monte Carlo simulation is given and a possible application to experimentally accessible systems is discussed.     

Towards a self-consistent theory of turbulent reconnection

Fast reconnection due to turbulent dissipation has long been hypothesized. This classic idea is critically examined in 3D reduced magnetohydrodynamic turbulence, by taking into account the backreaction of small-scale magnetic fields. We find that the backreaction leads to such a dramatic reduction in a global reconnection rate as to recover the original Sweet–Parker scaling. In 2D limit, the global reconnection rate is shown to be enhanced over the Sweet–Parker result by a factor of magnetic Mach number. These results are consequences of mean square magnetic potential balance.     

Crossover from BCS superconductivity to Bose-Einstein condensation: A self-consistent theory

A dilute three-dimensional Fermi liquid is considered with an instantaneous attractive short-range interaction. Two sets of self-consistent equations for the temperature dependent fermion Greens functiong and the four-point vertex function are derived by field theoretic means. The interaction is taken into account using the results of low energys-wave scattering theory. The crossover region between BCS superconductivity and Bose-Einstein condensation of tightly bound pairs is located near the threshold where in the two-particle scattering problem a virtual or quasi-stationary state turns into a bound state. We show how from our self-consistent equations the BCS theory and the theory of a superfluid Bose gas can be recovered in the weak and strong coupling limit, respectively. In the strong coupling limit we find that there is a repulsive interaction between the composite bosons due to the Pauli exclusion principle. It is described by a positive scattering lengtha _B which is twice the scattering length of the fermions,a _B =2a _F . Furthermore we find that this interaction reduces the Bose-Einstein transition temperature to leading order by T _c /T _{c, BE} =–(k _F a _F )³/3. We show that most of the previous theories of the crossover scenario can be obtained from our theory in mean-field approximation neglecting self consistency.     

A self-consistent theory for exchange and correlation effects in electron gas

A theory of electron correlations giving self-consistently the compressibility and spin susceptibility is formulated within the generalized random-phase approximation.     

Unstable particles in a self-consistent field theory

We indicate how unstable particles can be introduced into the self-consistent field theory formulation of Umezawa where the equal-time commutation relations for Heisenberg fields are derived and not assumed. The Lee model is used to illustrate the results.