Dirac-Schr\"odinger equation for quark-antiquark bound states and derivation of its interaction kerne

The four-dimensional Dirac-Schr\"odinger equation satisfied by quark-antiquark bound states is derived from Quantum Chromodynamics. Different from the Bethe-Salpeter equation, the equation derived is a kind of first-order differential equations of Schr\"odinger-type in the position space. Especially, the interaction kernel in the equation is given by two different closed expressions. One expression which contains only a few types of Green's functions is derived with the aid of the equations of motion satisfied by some kinds of Green's functions. Another expression which is represented in terms of the quark, antiquark and gluon propagators and some kinds of proper vertices is derived by means of the technique of irreducible decomposition of Green's functions. The kernel derived not only can easily be calculated by the perturbation method, but also provides a suitable basis for nonperturbative investigations. Furthermore, it is shown that the four-dimensinal Dirac-Schr\"odinger equation and its kernel can directly be reduced to rigorous three-dimensional forms in the equal-time Lorentz frame and the Dirac-Schr\"odinger equation can be reduced to an equivalent Pauli-Schr\"odinger equation which is represented in the Pauli spinor space. To show the applicability of the closed expressions derived and to demonstrate the equivalence between the two different expressions of the kernel, the t-channel and s-channel one gluon exchange kernels are chosen as an example to show how they are derived from the closed expressions. In addition, the connection of the Dirac-Schr\"odinger equation with the Bethe-Salpeter equation is discussed

Continuous Beams of Aluminum Alloy Tubular Cross Sections. I: Tests and FE Model Validation

The aims of this study are to generate experimental data and develop numerical models for aluminum alloy continuous beams, and to utilize the results to underpin the development of revised design methods for indeterminate structures. This paper presents an experimental program and finite-element (FE) analyses for two-span continuous beams (i.e., five-point bending) of square and rectangular hollow sections (SHSs and RHSs). The experimental program comprised 27 five-point bending tests with three different positioning of loads. The testing procedures and key results are reported. The test specimens were manufactured by extrusion, with 18 of grade 6061-T6 and 9 of grade 6063-T5 heat-treated aluminum alloys. The test specimens were nonslender sections, and mostly of Class 1 proportions. Generally, the specimens failed by the formation of a collapse mechanism comprising three plastic hinges. The distances between the supports and the loading points were varied in order to form the first plastic hinge in different locations, to achieve different load levels between the first hinge and collapse, and to change the rotation demands on the first hinge that formed. The FE models were developed and failure was defined as either when a plastic collapse mechanism was formed or the material fracture strain was reached on the tension flange, whichever occurred first. The numerical models were first validated against the experimentally obtained load-deflection responses, as well as the failure modes. The experimental and FE ultimate loads were both found to be beyond the theoretical loads corresponding to the formation of the first hinge as well as the calculated plastic collapse loads. A key characteristic of aluminum alloy, strain hardening, is shown to be particularly significant in both the experimental program and the numerical investigation. The validated FE models are used to generate numerical results through parametric studies in the companion paper. The development of design rules for indeterminate aluminum alloy structural systems is then described

Deformation-based design of aluminium alloy beams

Two series of simply supported bending tests on aluminium alloy square and rectangular hollow sections have been performed. The test program comprised 14 three-point bending tests and 15 four-point bending tests. The test specimens were fabricated by extrusion from grades 6061-T6 and 6063-T5 heat-treated aluminium alloys, with width-to-thickness ratios ranging from 2.8 to 20.5. Measured geometric and material properties, together with the full load–deflection histories from the test specimens, were reported. Observed failure modes included local buckling, material yielding and tensile fracture. Further experimental data were gathered from the literature. Finite element (FE) models were developed and validated against the test results, and then used to perform parametric studies, in which a total of 132 numerical results were generated. The experimental and numerical results were used to evaluate the bending resistance provisions of the American [1], Australian/New Zealand [2] and European [3] Specifications, as well as the continuous strength method (CSM). The moment capacities predicted by the three design specifications were found to be generally conservative, while the CSM provided more accurate and more consistent predictions due to the recognition and systematic exploitation of strain hardening

Calculation of gπNS11g_{\pi NS_{11}} and gηNS11g_{\eta NS_{11}} Couplings in QCD Sum Rules

We calculate the coupling constants, $g_{\pi NS_{11}}$ and $g_{\eta NS_{11}}, using QCD sum rules in the presence of an external meson field. A covariant derivative is introduced within the S_{11} interpolating field so that in the nonrelativistic limit the field dominantly reduces to two quarks in the s-wave state and one quark in the p-wave state. Our result for the couplings obtained by further making use of the soft-meson theorem qualitatively agrees with its phenomenological value extracted from the S_{11}(1535) decay width. The prediction for the couplings however depend on the value of quark-gluon condensate,$$, which is also important in the calculation of the S_{11}(1535) mass itself within the sum rule approach.Comment: 8 pages (no figure), revte

High-Q-factor Al [subscript 2]O[subscript 3] micro-trench cavities integrated with silicon nitride waveguides on silicon

We report on the design and performance of high-Q integrated optical micro-trench cavities on silicon. The microcavities are co-integrated with silicon nitride bus waveguides and fabricated using wafer-scale silicon-photonics-compatible processing steps. The amorphous aluminum oxide resonator material is deposited via sputtering in a single straightforward post-processing step. We examine the theoretical and experimental optical properties of the aluminum oxide micro-trench cavities for different bend radii, film thicknesses and near-infrared wavelengths and demonstrate experimental Q factors of > 10[superscript 6]. We propose that this high-Q micro-trench cavity design can be applied to incorporate a wide variety of novel microcavity materials, including rare-earth-doped films for microlasers, into wafer-scale silicon photonics platforms

Double-Diffusive Convection During Growth of Halides and Selenides

Heavy metal halides and selenides have unique properties which make them excellent materials for chemical, biological and radiological sensors. Recently it has been shown that selenohalides are even better materials than halides or selenides for gamma-ray detection. These materials also meet the strong needs of a wide band imaging technology to cover ultra-violet (UV), midwave infrared wavelength (MWIR) to very long wavelength infrared (VLWIR) region for hyperspectral imager components such as etalon filters and acousto-optic tunable filters (AO). In fact AOTF based imagers based on these materials have some superiority than imagers based on liquid crystals, FTIR, Fabry-Perot, grating, etalon, electro-optic modulation, piezoelectric and several other concepts. For example, broadband spectral and imagers have problems of processing large amount of information during real-time observation. Acousto-Optic Tunable Filter (AOTF) imagers are being developed to fill the need of reducing processing time of data, low cost operation and key to achieving the goal of covering long-wave infrared (LWIR). At the present time spectral imaging systems are based on the use of diffraction gratings are typically used in a pushbroom or whiskbroom mode. They are mostly used in systems and acquire large amounts of hyperspectral data that is processed off-line later. In contrast, acousto-optic tunable filter spectral imagers require very little image processing, providing new strategies for object recognition and tracking. They are ideally suited for tactical situations requiring immediate real-time image processing. But the performance of these imagers depends on the quality and homogeneity of acousto-optic materials. In addition for many systems requirements are so demanding that crystals up to sizes of 10 cm length are desired. We have studied several selenides and halide crystals for laser and AO imagers for MWIR and LWIR wavelength regions. We have grown and fabricated crystals of several materials such as mercurous chloride, mercurous bromide, mercurous iodide, lead chloride lead bromide, lead iodide, thallium arsenic selenide, gallium selenide, zince sulfide zinc selenide and several crystals into devices. We have used both Bridgman and physical vapor transport (PVT) crystal growth methods. In the past have examined PVT growth numerically for conditions where the boundary of the enclosure is subjected to a nonlinear thermal profile. Since past few months we have been working on binary and ternary materials such as selenoiodides, doped zinc sulfides and mercurous chloro bromide and mercurous bromoiodides. In the doped and ternary materials thermal and solutal convection play extremely important role during the growth. Very commonly striations and banding is observed. Our experiments have indicated that even in highly purified source materials, homogeneity in 1-g environment is very difficult. Some of our previous numerical studies have indicated that gravity level less than 10-4 (-g) helps in controlling the thermosolutal convection. We will discuss the ground based growth results of HgClxBr(1-x) and ZnSe growth results for the mm thick to large cm size crystals. These results will be compared with our microgravity experiments performed with this class of materials. For both HgCl-HgBr and ZnS-ZnSe the lattice parameters of the mixtures obey Vagard's law in the studied composition range. The study demonstrates that properties are very anisotropic with crystal orientation, and performance achievement requires extremely careful fabrication to utilize highest figure of merit. In addition, some parameters such as crystal growth fabrication, processing time, resolution, field of view and efficiency will be described based on novel solid solution materials. It was predicted that very similar to the pure compounds solid solutions also have very large anisotropy, and very precise oriented and homogeneous bulk and thin film crystals is required to achieve maximum performance of laser or imagers. Some of the parameters controlling the homogeneity such as thermos-solutal convection driven forces can be controlled in microgravity environments to utilize the benefits of these unique materials

Analytical Results for a Hole in an Antiferromagnet

The Green's function for a hole moving in an antiferromagnet is derived analytically in the long-wavelength limit. We find that the infrared divergence is eliminated in two and higher dimensions so that the quasiparticle weight is finite. Our results also suggest that the hole motion is polaronic in nature with a bandwidth proportional to $t/J \exp [-c (t/J)^2]$ ($c$ is a constant). The connection of the long-wavelength approximation to the first-order approximation in the cumulant expansion is also clarified.Comment: 12 papes, 2 figures available upon request, revte

Theory for Gossamer and Resonating Valence Bond Superconductivity

We use an effective Hamiltonian for two-dimensional Hubbard model including an antiferromagnetic spin-spin coupling term to study recently proposed gossamer superconductivity. We formulate a renormalized mean field theory to approximately take into account the strong correlation effect in the partially projected Gutzwiller wavefucntions. At the half filled, there is a first order phase transition to separate a Mott insulator at large Coulomb repulsion U from a gossamer superconductor at small U. Away from the half filled,the Mott insulator is evolved into an resonating valence bond state, which is adiabatically connected to the gossamer superconductor.Comment: 10 pages, 13 figure

Time-Dependent Spin-Polarized Transport Through a Resonant Tunneling Structure with Multi-Terminal

The spin-dependent transport of the electrons tunneling through a resonant tunneling structure with ferromagnetic multi-terminal under dc and ac fields is explored by means of the nonequilibrium Green function technique. A general formulation for the time-dependent current and the time-averaged current is established. As its application the systems with two and three terminals in noncollinear configurations of the magnetizations under dc and ac biases are investigated, respectively. The asymmetric factor of the relaxation times for the electrons with different spin in the central region is uncovered to bring about various behaviours of the TMR. The present three-terminal device is different from that discussed in literature, which is coined as a spin transistor with source. The current-amplification effect is found. In addition, the time-dependent spin transport for the two-terminal device is studied. It is found that the photonic sidebands provide new channels for the electrons tunneling through the barriers, and give rise to new resonances of the TMR, which is called as the photon-asisted spin-dependent tunneling. The asymmetric factor of the relaxation times is observed to lead to additional resonant peaks besides the photon-asisted resonances.Comment: 32 pages,14 figure