E 6,7,8 magnetized extra-dimensional models

We study 10D super Yang–Mills theory with the gauge groups E ₆, E ₇ and E ₈. We consider the torus/orbifold compactification with magnetic fluxes and Wilson lines. They lead to 4D interesting models with three families of quarks and leptons, whose profiles in extra dimensions are quasi-localized because of magnetic fluxes.     

The Intermediate Vertex Subalgebras of the Lattice Vertex Operator Algebras

A notion of intermediate vertex subalgebras of lattice vertex operator algebras is introduced, as a generalization of the notion of principal subspaces. Bases and the graded dimensions of such subalgebras are given. As an application, it is shown that the characters of some modules of an intermediate vertex subalgebra between E ₇ and E ₈ lattice vertex operator algebras satisfy some modular differential equations. This result is an analogue of the result concerning the “hole” of the Deligne dimension formulas and the intermediate Lie algebra between the simple Lie algebras E ₇ and E ₈.     

Size-dependent threshold fields for Fröhlich conduction in niobium triselenide: Possible evidence for pinning by the crystal surface

The threshold field E_T for nonlinear “Fröhlich” conduction in niobium triselenide has been found to be correlated with the cross-sectional dimensions of the specimen. In 28 specimens from the same batch, E_T at 110 K was approximately proportional, over a range approaching 50 to 1, to the ratio C/A, where C is the circumference and A the area of the cross-section. No significant correlation was found between E_T and the resistance ratio R(293 K)/R(4.2 K), which was measured in 20 of the specimens and averaged 45. The diffraction evidence that the transverse phase coherence of the charge-density wave extends only over much smaller distances makes it unlikely that the cross-sectional dimensions influence E_T by limiting the Lee-Rice characteristic length for weak pinning by impurities. It is proposed that the pinning responsible for E_T is provided by the external surface of the crystal, supplemented in some cases by internal faults, rather than by impurities or other point defects within it.     

The integrability of N=16 supergravity

For the maximally extended N=16 supergravity theory in two dimensions, we explicitly construct a linear system whose integrability conditions are equivalent to the full nonlinear field equations of this theory. All the (on-shell) information contained in it can thus be encoded into a single E₈ matrix and its dependence on a spectral parameter; the invariance of the equations of motion under E₉ is manifest. Possible consequences and further developments are briefly discussed.     

Small E8 instantons and tensionless non-critical strings

T-duality is used to extract information on an instanton of zero size in the E₈ × E₈ heterotic string. We discuss the possibility of the appearance of a tensionless anti-self-dual non-critical string through an implementation of the mechanism suggested by Strominger of two coincident 5-branes. It is argued that when an instanton shrinks to zero size a tensionless non-critical string appears at the core of the instanton. It is further conjectured that the appearance of tensionless strings in the spectrum leads to new phase transitions in six dimensions in much the same way as massless particles do in four dimensions.     

Influence of the boundary conditions on the fermi energy and density of states in a free-electron solid of sub-micron dimensions

Asymptotic expressions for the distribution of the eigenvalues of the Helmholtz-Schrödinger equation are used to anlyze the dependence of the Fermi energy, E_F, and the density of states, ρ(E), on sample size, shape, and electron density, in a free-electron model with Dirichlet boundary conditions. It is found that for very small samples E_F is increased relative to its asymptotic (i.e., bulk) value and ρ(E) is decreased relative to its bulk value. These effects are more pronounced for samples with low electron density and with a large surface-to-volume ratio. In general E_F and ρ(E_F) deviate significantly from their bulk values only for systems with fewer than 50,000 electrons and/or with linear dimensions of 100 Å or less. The use of smoothing functions to represent the density of states obtained from the exact eigenvalue distribution is also discussed. It is shown that an oscillating density of states leads to small cusps in the plot of E_F as a function of sample size. This is in qualitative agreement with the results of experiments on size-dependent oscillations in field emission from thin metallic films. Comparison is also made between photoemission experiments from thin films and other results obtained in this study.     

The two-dimensional Falicov-Kimball model at finite temperatures: numerical studies

The finite temperature properties of the spinless Falicov-Kimball model are studied in two dimensions using small-cluster exact-diagonalization calculations. The resultant exact solutions are used to examine the f-state occupation (n _f), the specific heat (C) and the density of doubly occupied sites (d) as functions of temperature (τ), f-level energy (E _f) and the interaction strength U. A number of remarkable results are found. (i) In all cases nf and d are smooth functions of τ and E _f. No discontinuous transitions occur at finite temperatures. (ii) The specific-heat curves exhibit a broad single-peak structure of Shottky form (‖E _f‖ large), as well as a two-peak structure consisting of a sharp peak of Ising type followed by a broad peak of Shottky type (‖E _f‖ small). (iii) The specific-heat coefficient is extremely enhanced at low temperatures for some values of E _f. (iv) Depending on a range of parameters used, the system exhibits intermediate-valence behavior as well as some features of heavy-fermion behavior. The results are independent of the size of clusters for a wide range of parameters and can be used to interpret much of the experimental data of rare-earth compounds. Finally, the f-electron density-density correlation functions are calculated and the U-dependence of the critical temperature is discussed.     

Calculation of gauge couplings and compact circumferences from self-consistent dimensional reduction

We consider a system of gravity plus free massless matter fields in 4 + N dimensions, and look for solutions in which N dimensions form a compact curved manifold, with the energy-momentum tensor responsible for the curvature produced by quantum fluctuations in the matter fields. For manifolds of sufficient symmetry (including spheres, CP^N, and manifolds of simple Lie groups) the metric depends on only a single multiplicative parameter ?², and the field equations reduce to an algebraic equation for ?, involving the potential of the matter fields in the metric of the manifold. With a large number of species of matter fields, the manifold will be larger than the Planck length, and the potential can be calculated using just one-loop graphs. In odd dimensions these are finite, and give a potential of form C_N/?⁴. Also there are induced Yang-Mills and Einstein-Hilbert terms in the effective 4-dimensional action, proportional to additional numerical coefficients, D_N and E_N. General formulas are given for the gauge coupling g² in terms of C_N and D_N, and the ratio ?²/8πG in terms of C_N and E_N. Numerical values for C_N, D_N, and E_N are obtained for scalar and spinor fields on spheres of odd dimensionality N. It is found that the potential, g² and ?²/8πG can all be positive but only when the compact manifold has N = 3 + 4 k dimensions. (The positivity of the potential is needed for stability of the sphere against uniform dilations or contractions). In this case, solutions exist either for spinor fields alone or for suitable mixes of spinor and scalar fields provided the ratio of the number of scalar fields to the number of fermion fields is not too large. Numerical values of the O(N + 1) gauge couplings and 8φG/?² are calculated for illustrative values of the numbers of spinor fields. It turns out that large numbers of matter fields are needed to make these parameters reasonably small.     

On generalized Yang-Mills theories and extensions of the standard model in Clifford (tensorial) spaces

We construct the Clifford-space tensorial-gauge fields generalizations of Yang-Mills theories and the Standard Model that allows to predict the existence of new particles (bosons, fermions) and tensor-gauge fields of higher-spins in the 10 Tev regime. We proceed with a detailed discussion of the unique D₄ − D₅ − E₆ − E₇ − E₈ model of Smith based on the underlying Clifford algebraic structures in D = 8, and which furnishes all the properties of the Standard Model and Gravity in four-dimensions, at low energies. A generalization and extension of Smith’s model to the full Clifford-space is presented when we write explicitly all the terms of the extended Clifford-space Lagrangian. We conclude by explaining the relevance of multiple-foldings of D = 8 dimensions related to the modulo 8 periodicity of the real Cliford algebras and display the interplay among Clifford, Division, Jordan, and Exceptional algebras, within the context of D = 26, 27, 28 dimensions, corresponding to bosonic string, M and F theory, respectively, advanced earlier by Smith. To finalize we describe explicitly how the E₈ × E₈ Yang-Mills theory can be obtained from a Gauge Theory based on the Clifford (16) group.     

Effects of annealing on localized states in amorphous Ge films

Annealing behaviors of the activation energy for the electrical conduction E_σ, that for the thermoelectric power E_s, the optical gap E^opt_g, and the spin density in evaporated amorphous Ge are investigated. E_σ is independent of E_s and E^opt_g, and the rates of variation of E^opt_g and E_s with annealing temperature are connected by △E^opt_g = 2.5△E^opt_s. It is suggested that the position of the Fermi level does not change with annealing in contrast with amorphous Si, and the edge of the localized tail state shifts with annealing.     

Hopping conductivity of carbynes modified under high pressures and temperatures: Galvanomagnetic and thermoelectric properties

The conductivity, thermopower, and magnetoresistance of carbynes structurally modified by heating under a high pressure are investigated in the temperature range 1.8–300 K in a magnetic field up to 70 kOe. It is shown that an increase in the synthesis temperature under pressure leads to a transition from 1D hopping conductivity to 2D and then to 3D hopping conductivity. An analysis of transport data at T ≤ 40 K makes it possible to determine the localization radius a ～ (56?140) Å of the wave function and to estimate the density of localized states _g(E _F) for various dimensions d of space: _g(E _F) ≈ 5.8 × 10⁷ eV^?1 cm^?1 (d=1), _g(E _F) ≈5×10¹⁴ eV^?1 cm ^?2 (d=2), and _g(E _F)≈1.1×10²¹ eV^?1 cm_?3 (d=3). A model for hopping conductivity and structure of carbynes is proposed on the basis of clusterization of sp ² bonds in the carbyne matrix on the nanometer scale.     

Intracellular potential relief and size effects in the lattice of a LaF3 superionic conductor

The potential relief in the lattice of a LaF₃ crystal is calculated by quantum-mechanical methods for clusters containing from 24 to 1200 ions. For the dielectric phase, formation energy E _a for defects of the vacancy-interstitial fluorine ion type and potential barrier E _d preventing the motion of fluorine ions are found to grow from minimal values E _a = 0.12 eV and E _d = 0.22 eV for a cluster of 24 ions to maximal values E _a = 0.16 eV and E _d = 0.26 eV for clusters of 576 and 1200 ions. The values of E _a and E _d obtained in quasi-mechanical calculations are in good agreement with those obtained from Raman and quasi-elastic light scattering data.     

New bounds for dilepton production from heavy neutral leptons

Bounds on 〈E_?ⁿ〉/〈E₊ⁿ〈, 〉E₊E_?〈/〉E₂²〈 and 〈E₊E_?〉/〈E₊〉〈E_?〉 are direved for the processes ν_μN → μ^?μ⁺(e⁺) + X and μN → μ^?μ⁺ + X if dileptons are mediated by a $\text{spin}\text{-}\text{1}\text{2}$ heavy neutral lepton L₀. The bounds are shown to be independent of the production mechanism and mass of L₀. Useful conditional bounds are obtained relating the bounded quantities, which give information about the structure of the weak current responsible for L₀ decay.     

High-resolution electroreflectance measurements of GaAs

High-resolution surface-barrier electroreflectance measurements are reported for GaAs, taken at 4.2 K in the Schottky barrier configuration. Interference effects between the bulk and space-charge regions are seen at the n = 1 exciton line for both E₀ and E₀ + Δ₀ transitions. We calculate the value μ_T = (0.055 ± 0.008) m_e for the transverse mass of the E₁ + Δ₁ transition from Franz-Keldysh oscillations observed at high fields. The E'₀ structure is resolved into separate critical points of Γ and Δ symmetry. Threshold and broadening energies are obtained at 4.2 K for the E₀,E₀, E₀ + Δ₀, E₁, E₁ + Δ₁, E'₀ (Γ and and E₂ (Σ and X) critical points.     

Effect of conduction band nonprabolicity on the Rashba spin splitting of AlGaN/GaN QWs

By using the perturbation expansion method and self-consistent iterative method, we evaluate the effect of the conduction band nonprabolicity on the wave vector (k_t) dependent Rashba coefficient (α) and nonlinear Rashba spin splitting (ΔE) in the Al_0.5Ga_0.5N/GaN quantum well (QW). The effective mass (energy) under the first order approximation m_t1 (E_k1) is in proximity to the iterative result m_tp (E_kp) and m_t1>m_tp, E_k1<E_kp, showing the higher order contributions to m_t (E_k) are small. The sign of the nonparabolic correction to E_k is just opposite to that of the correction to m_t. The increase of α and ΔE due to the conduction band nonparabolicity reaches about 3% at k_t=1 nm⁻¹. Around the left heterointerface, the probability density is high and E_k0>E_kp>E_k1, so α₀<α_p<α₁, ΔE₀<ΔE_p<ΔE₁. With increasing k_t, α decreases, and ΔE increases slowly. For small k_t, α₀ (ΔE₀), α₁ (ΔE₁) and α_p (ΔE_p) are nearly the same. While for large k_t, the difference between α₀ and α₁ (α_p) increases rapidly, but the difference between ΔE₀ and ΔE₁ (ΔE_p) increases slowly.     

Synthesis of single crystal CuAlS2 nanowires via a low temperature direct polyol route

The direct polyol method is used to prepare copper aluminium sulfide CuAlS₂ nanowires. The lattice constants of CuAlS₂ nanowires calculated from powder X-ray diffraction data indicates chalcopyrite structure. The CuAlS₂ nanowires are uniformly in shape and their dimensions are about 50 nm in diameter and several of micrometers in length. The Photoluminescence (PL) spectrum of CuAlS₂ nanowires show a sharp absorption edge at 358.96 nm and a strong near band edge emission at 3.46 eV. The direct energy gap Eg of the sample has been calculated as 3.48 eV, that corresponding to the photoluminescence study. A possible formation mechanism of copper aluminium sulfide is proposed.     

Optical properties of lithium barium haloborate glasses

Lithium haloborate glasses have been prepared according to the formula (70−y)B₂O₃-30BaF2-yLiX where y=0, 5, 10, 15 and 20 mol% and X=F, Cl and Br. The UV absorption spectra have been recorded at room temperature. The optical energy band gap E_opt and Urbach energy E_tail was determined. Increasing concentration of LiX in the glass shifts the UV cutoff to lower energy and decreases both E_opt and E_tail. The shift in UV cutoff and the decrease of E_opt and E_tail are maximum in the range 0-5 mol% LiX. The decrease of E_opt increases going from F, Cl to Br, whereas the decrease of E_tail increases going from Br, Cl to F. At higher LiX concentrations Urbach energy E_tail increases again. The behavior of E_opt has been correlated with the B-O bond length of the studied glasses. The decrease of E_opt and E_tail is due to the increase of nonbridging oxygen (NBO) concentration with increase of LiX content. The increase of E_tail at higher concentrations is attributed to the halide ion accumulation in the interstitial positions and to the formation of orthoborate groups. Refractive index, which is measured and calculated, molar refraction and polarizability are all correlated with the composition of the glasses.     

Compactification on non-symmetric six dimensional coset spaces with torsion

The equations of motion of a ten dimensional model based on the Chapline-Manton lagrangian, modified by higher derivative terms, are solved using six dimensional coset spaces with torsion. Minkowski space, anti-de Sitter, de Sitter and Einstein static cosmology with negative curvature are possible four dimensional cosmologies. In all case symmetry breaking schemesE ₈×E ₈→E ₈×E ₆ with chiral 27's ofE ₆ can be obtained.     

Lower and upper variational bounds in calculations of Coulomb and nuclear systems

All formulas that are necessary for deriving not only upper (E _U) but also lower (E _L) variational bounds on the energy of systems featuring a few nonrelativistic particles are obtained with trial functions in the form of expansions in multidimensional Gaussian functions or exponentials. For potentials that are used most widely, all matrix elements are expressed in terms of known functions, a circumstance that simplifies considerably relevant numerical calculations. This is so for systems featuring an arbitrary number of particles in the case of a Gaussian basis and for three-particle systems in the case of an exponential basis. Numerical results for E _U and E _L, which are characterized by record accuracies, are presented for some Coulomb and nuclear systems such as the He atom; the e ⁺ e ^? e ^?, ppμ^?, 3α, and 4α systems; and hypertritium (pnΛ). Lower bounds with exponential trial functions are obtained for the first time (the corresponding formulas are presented for the first time as well); for a Gaussian basis, lower bounds for Coulomb systems have not been known either. Given E _L and E _U, limits within which the exact value of energy, E ₀, lies can be indicated with confidence. Moreover, an analysis of the correlation between E _L and E _U with increasing number of terms in the expansion of the trial function makes it possible to improve the accuracy (at least by one order of magnitude) of the value E _∞ extrapolated to infinity. By considering specific examples, it is shown that the exponential basis is advantageous in relation to the Gaussian one.     

E11 as E10 representation at low levels

The Lorentzian Kac–Moody algebra E₁₁, obtained by doubly overextending the compact E₈, is decomposed into representations of its canonical hyperbolic E₁₀ subalgebra. Whereas the appearing representations at levels 0 and 1 are known on general grounds, higher level representations can currently only be obtained by recursive methods. We present the results of such an analysis up to height 120 in E₁₁ which comprises representations on the first five levels. The algorithms used are a combination of Weyl orbit methods and standard methods based on the Peterson and Freudenthal formulae. In the appendices we give all multiplicities of E₁₀ occurring up to height 340 and for E₁₁ up to height 240.