Self-consistent theory of localization for the Anderson model

The self-consistent theory of electron localization in a random system in the form proposed by Vollhardt and Wölfle is generalized for the analysis of localization in the Anderson model. We derive the general equations appropriate for the system with rather general form of the electronic spectrum. Explicit calculations are restricted to the lattices of cubic symmetry and use the effective mass approximation to obtain the final results. Anderson's critical ratio for the localization of all the electronic states in the tight-binding band is evaluated and found to be in surprisingly good agreement with the results of numerical analysis of localization in the Anderson model.     

Self-consistent theory of localization in weakly disordered systems

An analytic treatment of localization in a weakly disordered system is presented for the case where the real lattice is approximated by a Cayley tree. Contrary to a recent assertion we find that the mobility edge moves inwards into the band as disorder increases from zero.     

Self-consistent theory of population,ionization and electron distribution

We derive analytical formulae for population of excited levels and degree of ionization of atoms not necessarily restricted to the Maxwellian distribution of the free electrons. The results are obtained from solving Boltzmann's equation with a simplified form of the inelastic collision term. Good agreement with numerical results of other authors is obtained.     

Self-consistent perturbation theory

The density matrix form of Hartree-Fock perturbation theory is developed for the case in which the basis functions themselves are perturbation-dependent. Energy expressions are derived, through second order, for both single and double perturbations.

The theory is applied in the calculation of electric dipole polarizabilities and hyperpolarizabilities for atoms (He, Be) and molecules (H₂, LiH), with excellent results. The high computational efficiency of the method is discussed and possibilities of further development are outlined.     

Self-consistent scaling theory for logarithmic-correction exponents

Multiplicative logarithmic corrections frequently characterize critical behavior in statistical physics. Here, a recently proposed theory relating the exponents of such terms is extended to account for circumstances which often occur when the leading specific-heat critical exponent vanishes. Also, the theory is widened to encompass the correlation function. The new relations are then confronted with results from the literature, and some new predictions for logarithmic corrections in certain models are made.     

Self-consistent field theory and calculation for gyromonotron

A self consistent field large signal theory of gyromonotron is studied in this paper. The RF field profile function satisfies a wave equation. The field is determined by cavity geometry and AC electron beam current. The RF field not only satisfies the boundary conditions at the ends of the cavity but also obeys conservation of energy for steady state interaction between electron beam and field. The parameters of a particular gyrotron are calculated numerically using present theory. Effect of some factors on gyrotron characteristic is discussed. Comparison is made between the results of the self consistent field calculations with and without conservation of energy.     

Self-consistent Hückel theory

Systematic approximations to the Pople method lead to a form of Hückel theory which is self-consistent with respect to charges and bond orders. The method is applied to the calculation of ionization potentials, electron affinities and equilibrium bond lengths in conjugated molecules.     

Self-consistent perturbation theory for dynamics of valence fluctuations

Dynamical properties of valence-fluctuating systems are studied at absolute zero of temperature. The self-consistent perturbation theory developed for rare-earth impurity systems is used with some refinement. The theory takes account of the orthogonality catastrophe caused by hybridization of 4f and conduction electrons. Extensive numerical results are reported for the 4f-electron density of states _4f () and the dynamical magnetic susceptibility (). The results cover both the intermediate-valence and nearly integral-valence regimes of a model Ce impurity system. The present theory gives reasonable overall feature of dynamics including a sharp peak in _4f (0) in the Kondo regime. However, the low-frequency limit of dynamical quantities is not consistent with the Fermi-liquid property. It is shown that interpolation of the present results and those by the Fermi-liquid theory is possible. Hence accurate dynamical information is obtained over a wide excitation-frequency range.     

Self-consistent perturbation theory for dynamics of valence fluctuations

Dynamical property of an intermediate-valence Tm ion in a metallic matrix is investigated by the use of the self-consistent perturbation theory. Both of the fluctuating valence states in Tm have nonzero angular momentum in contrast to Ce and Yb systems. It is shown that the participation of two valence states in the magnetic susceptibility leads to peculiar magnetic properties such as enhanced Korringa-type magnetic relaxation and a systematic deviation from the Curie-Weiss law of the susceptibility. The susceptibility diverges in the zero-temperature limit. The dynamical susceptibility can be fitted by the Lorentzian lineshape very well for a wide frequency and temperature range. The single-particle excitation spectrum is also derived from which the resistivity is calculated. A logarithmic increase of the resistivity with decreasing temperature is found.     

Self-consistent theory of screening in a two dimensional electron gas under strong magnetic field

The dielectric response of a two dimensional electron gas under a strong transverse magnetic field is obtained within a self-consistent procedure in which the broadening of Landau levels due to collisional damping from the impurities both determines and is determined by the static dielectric function of the system. The dielectric function is evaluated in random phase approximation with the impurity scattering treated in a self-consistent Born approximation. Explicit results are presented for the zero temperature, extreme quantum limit. It is found that this “no parameter” theory is in good qualitative agreement with experimental results for the broadening as extracted from magnetotransport data.     

Self-consistent theory of Bose-condensed systems

In the theory of Bose-condensed systems, there exists the well known problem, the Hohenberg–Martin dilemma of conserving versus gapless approximations. This dilemma is analysed and it is shown that it arises because of the internal inconsistency of the standard grand ensemble, as applied to Bose systems with broken global gauge symmetry. A solution of the problem is proposed, based on the notion of representative statistical ensembles, taking into account all constraints imposed on the system. A general approach for constructing representative ensembles is formulated. Applying a representative ensemble to Bose-condensed systems results in a completely self-consistent theory, both conserving and gapless in any approximation.     

Self-consistent perturbation theory for dynamics of valence fluctuations

A perturbation-theoretic scheme is developed for dynamics of valence fluctuations in rare-earth systems with unstable 4f shells. The theory is formulated in close analogy to the standard Green-function method for many-body systems but without use of the linked-cluster theorem. This formulation regards hybridization between 4f and conduction-band states as perturbation and naturally incorporates the strong on-site 4f-electron correlation. Some favorable features are: (i) the approximation scheme automatically satisfies conservation laws required for response functions; (ii) realistic 4f-shell structures with crystalline-electric-field effects can be taken into account; (iii) the theory does not have divergence difficulties over the whole temperature range. In the lowest-order self-consistent approximation, explicit formulae for dynamical susceptibilities and 4f-electron density of states are presented. At high temperatures, the theory reproduces previous results obtained by the Mori method.     

Self-consistent perturbation theory for dynamics of valence fluctuations

Dynamical as well as equilibrium properties of model Ce systems are investigated in both the intermediate-valence and nearly integral-valence (Kondo) regimes at finite temperatures. With self-consistent account of hybridization effects between the conduction bands and the highly correlated 4f states, the 4f-electron density of states _4f () and the dynamical magnetic susceptibility () are derived. Equilibrium properties such as the static magnetic susceptibility and the averaged 4f-electron number are also computed within the same approximation scheme that neglects intersite interactions between different Ce ions. In the intermediate-valence regime the calculated line-shape of Im ()/ is close to the Lorentzian at high temperatures, but at low temperatures there appears an inelastic peak. In the Kondo regime it is shown that a sharp peak in _4f () develops at the Fermi level as the temperature decreases. The line-shape of Im ()/ is shown to be close to the Lorentzian at all temperatures. The half-width is considerably enhanced over the Korringa value expected for the local-moment system. The temperature dependence of the half-width agrees qualitatively with experimental results in Kondo compounds such as CeB₆, CeCu₂Si₂ and CeAl₃.