Superconductivity in a two dimensional extended Hubbard model

The Roth’s two-pole approximation has been used by the present authors to investigate the role of d-p hybridization in the superconducting properties of an extended d-p Hubbard model. Superconductivity with singlet -wave pairing is treated by following Beenen and Edwards formalism. In this work, the Coulomb interaction, the temperature and the superconductivity have been considered in the calculation of some relevant correlation functions present in the Roth’s band shift. The behavior of the order parameter associated with temperature, hybridization, Coulomb interaction and the Roth’s band shift effects on superconductivity are studied.     

Spontaneous symmetry breaking and Higgs' mechanism in the nonsymmetric Kaluza-Klein theory

The nonsymmetric Kaluza-Klein theory unifying Moffat's theory of gravitation, the Yang-Mills' field and the Higgs' fields are constructed in a geometric manner. Spontaneous symmetry breaking, the Higgs' mechanism and mass generation in the theory are discussed. The connection between R₊ invariance (dilatation on the space-time) from Moffat's theory of gravitation and U(1)_F from GUTs, is proposed within the framework of fermion number conservation.     

First digit law from Laplace transform

The occurrence of digits 1 through 9 as the leftmost nonzero digit of numbers from real-world sources is distributed unevenly according to an empirical law, known as Benford's law or the first digit law. It remains obscure why a variety of data sets generated from quite different dynamics obey this particular law. We perform a study of Benford's law from the application of the Laplace transform, and find that the logarithmic Laplace spectrum of the digital indicator function can be approximately taken as a constant. This particular constant, being exactly the Benford term, explains the prevalence of Benford's law. The slight variation from the Benford term leads to deviations from Benford's law for distributions which oscillate violently in the inverse Laplace space. We prove that the whole family of completely monotonic distributions can satisfy Benford's law within a small bound. Our study suggests that the origin of Benford's law is from the way that we write numbers, thus should be taken as a basic mathematical knowledge.     

Thermodynamic properties of small extended Hubbard rings

We have obtained the exact numerical results of the specific heat, the susceptibility and the correlation functions L₀(T) and L₁(T) for finite extended Hubbard rings at the large U limit. It is shown that the nearest neighbor interactions favor the ferromagnetic ordering. When the number of electrons is less than the number of sites, the electron hopping results in itinerant magnetism and washes out the high temperature peak (around T = U/k_B) in the specific heat. In all cases, the behaviors of L₀(T) and L₁(T) are consistent with the characteristic features of the specific heat and the susceptibility. Thd exact results are used to test the accuracy of the Roth's decoupling scheme.     

First order green-function theory of isotropic Heisenberg ferromagnet

The Heisenberg ferromagnet with general spin S is considered within Green-function theory and spectral density method. New difference equations of the first order determining one- and two-particle correlation functions are derived and solved. The spectral density method is used to close Oguchi's variational theory without additional decoupling assumptions. The temperature renormalized spectrum is found to be a series expansion in that the first term coincide with RPA result and the first two terms correspond essentially to Callen's result. Low temperature expansions for the renormalization factor and the magnetization are given and shown to coincide with Callen's result.     

Non-physical three magnon states of Dyson's Hamiltonian

Non-physical three magnon states at real energy of Dyson's Hamiltonian are found. In the two-, and three-dimensional s.c. lattice these states lie within the physical continuum.     

Geometric dependence of casimir energy and scalar green's functions

It is well known that the Casimir Energy depends on the geometry of the conducting cavity. In this note, scalar Green's functions are used to determine the Casimir energy's dependence on terms bilinear in the extrinsic curvatures of the cavity's surface, and thus to resolve the controversy over the Casimir energy's finiteness.     

Relativistic Boltzmann theory for a plasma: II. Reciprocal relations

The linear or phenomenological laws such as Ohm's law, Fourier's law and Fick's law are derived for a relativistic plasma in an electromagnetic field. It is shown that the choice of a reference frame as proposed by Landau and Lifshitz entails-in contrast to, for instance, the choice of Eckart-the validity of Onsager's reciprocity relations.     

Electronic spectra of carotenoids. Schiff's bases of carotenal and carotenones

Visible absorption bands of β-apo-8′-carotenal, citranaxanthin, and reticulataxanthin Schiff's bases are measured and analyzed in relation to the visual chromophore, retinal Schiff's base. The former shows a strong red shift of the absorption maxima upon protonation in ethanol, and the magnitude of the band shift is comparable to that of retinal Schiff's base. Molecular orbital analysis of the ground and excited state electronic structures of both types of Schiff's bases suggests the usefulness of carotenal Schiff's bases as a model for comparative studies with visual chromophore.     

Valence band state densities of tetrahedrally coordinated amorphous semiconductors

A novel technique, for obtaining the valence band state densities (VBSD's) of tetrahedrally coordinated amorphous semiconductors from normal incidence reflectance data, is applied to Si and Ge and GaP, GaAs and GaSb. The VBSD's of Si and Ge are similar to other published results, obtained by conventional techniques, and cannot be described by broadened crystalline VBSD's. On the other hand, the VBSD's of the 3–5's contain many of the crystalline features. The relation of these results to the structure of the amorphous phase is discussed.     

Poisson's ratio for polycrystals

Accepted views concerning Poisson's ratio for central-force polycrystals are amended. For pulycrystals the ratio can vary from 1/4, which is actually a lower limit. An upper limit of Poisson's ratio exists also. Both limits can be calculated from single-crystal elastic data. The limits correspond to Voigt's and Reuss's states of uniform local strain and of uniform local stress, respectively.     

Justification of the local space charge neutrality hypothesis in metal oxidation

The important local charge neutrality hypothesis in metal oxidation theory is shown numerically to be self-consistent with Poisson's equation and the coupled transport equations for diffusion of oppositely-charged ionic and electronic defect species deep within very thick growing oxides.     

Calculation of the vertical ionization potentials of HCNO,HNCO, HOCN,and HN3 by perturbation corrections to Koopmans'Theorem

Vertical ionization potentials (VIP's) have been calculated for HCNO, HNCO, HOCN, and HN₃, using Rayleigh—Schrödinger perturbation theory (RSPT) to determine corrections to Koopmans' Theorem. The calculated VIP's are used to resolve discordances between previous assignments of the PE spectra of HCNO, HNCO, and HN₃. Very little is known about HOCN. The present work contains predicted VIP's for this molecule, which it is hoped will aid in its identification in the laboratory. A diagram is presented correlating the VIP's of the isoelectronic series N₂O, HN₃, HOCN, HNCO, HCNO, and CO₂. It is shown that the variation in the magnitudes of the VIP's associated with the ionization of π electrons, and in the splittings induced in these VIP's by deviations from a linear geometry, can be accounted for qualitatively using a simple Hückel model.     

The dynamic analysis of circular plates and shallow spherical shells

In the investigation reported here an attempt has been made to study the influence of Berger's approximation on the non-linear transient response of circular plates and shallow spherical shells. The governing equations of motion obtained from Berger's approximation are solved by using the rapidly converging Chebyshev series spacewise and the Houbolt scheme for integration in the time domain. Results calculated when using Berger's approximation are compared with exact results. It is shown that Berger's method yields very accurate values for plates and shells under transient loading, in the case of immovable edge conditions.     

Generalized Noether's theorem. I. theory

This article is a theoretical investigation of generalized Noether's theorem, which, though unconcerned with considerations such as coordinate transformations, symmetry, and invariance, is the basic mechanism of conventional Noether's theorem, its extensions, and its inverse. The generalized theorem is a completely new approach to the subject—formally, conceptually, and practically. It is an association, for a set of field equations, of field variations with conserved currents. The theorem is stated from two points of view and analyzed with regard to its interpretation and its formal and conceptual relation to conventional Noether's theorem and extensions, transformation groups, and Hamilton's principle. The inverse theorem is also treated. The role of coordinate transformations in conventional Noether's theorem is analyzed.     

Mechanical forces acting within non-polar fluid dielectrics

We compare Kelvin's polarization theory with Helmholtz's energy method for calculating forces in non-polar fluid dielectrics and show that in general they give different results and that only Helmholtz's method stands on firm foundations. We also discuss these results in connection with experiments and conclude that further experiments are needed to clarify the situation.     

On magnetic quantum oscillations of the Auger transition rate in narrow gap semiconductors

The experimental results of Dornhaus et al. on the dependence of the Auger recombination time on an applied magnetic field are explained within the frame of Takeshima's model by a proper inclusion of non-parabolicity and spin-splitting of the conduction band.     

Electromagnetic scattering from a spatially dispersive sphere

The problem of the scattering of a plane, monochromatic, linearly polarized, electromagnetic wave incident from vacuo onto a linear, homogeneous, non-magnetic, spatially dispersive sphere whose dielectric function is of the form is solved within the framework of Maxwell's theory.     

On the asymptotic eigenvalues of an inhomogeneous circular waveguide

An asymptotic formula is presented by means of which WKB's eigenvalues of a circular waveguide can be corrected in analytic form. Maslov's formula derived in 1960 for the determination of Schrödinger's eigenvalues is given for comparison. Both results are shown to be in complete agreement in a specific case.     

A comparison of some shell theories used for the dynamic analysis of cross-ply laminated circular cylindrical panels

The free vibration problem of thin elastic cross-ply laminated circular cylindrical panels is considered. For this problem, a theoretical unification as well as a numerical comparison of the thin shell theories most commonly used (in engineering applications) is presented. In more detail, the problem is formulated in such a way that by using some tracers, which have the form of Kronecker's deltas, the stress-strain relations, constitutive equations and equations of motion obtained produce, as special cases, the corresponding relations and equations of Donnell's, Love's, Sanders' and Flugge's theories. By using a closed form solution, obtained for simply supported panels, a comparison of corresponding numerical results obtained on the basis of all of the aforementioned shell theories is attempted.