Representations of the discrete inhomogeneous Lorentz group and Dirac wave equation on the lattice

We propose the fundamental and two dimensional representation of the Lorentz groups on a (3+1)-dimensional hypercubic lattice, from which representations of higher dimensions can be constructed. For the unitary representation of the discrete translation group we use the kernel of the Fourier transform. From the Dirac representation of the Lorentz group (including reflections) we derive in a natural way the wave equation on the lattice for spin 1/2 particles. Finally the induced representation of the discrete inhomogeneous Lorentz group is constructed by standard methods and its connection with the continuous case is discussed.Comment: LaTeX, 20 pages, 1 eps figure, uses iopconf.sty (late submission

Raising and lowering operators and their factorization for generalized orthogonal polynomials of hypergeometric type on homogeneous and non-homogeneous lattice

We complete the construction of raising and lowering operators, given in a previous work, for the orthogonal polynomials of hypergeometric type on non-homogeneous lattice, and extend these operators to the generalized orthogonal polynomials, namely, those difference of orthogonal polynomials that satisfy a similar difference equation of hypergeometric type.Comment: LaTeX, 19 pages, (late submission to arXiv.org

Raising and lowering operators, factorization and differential/difference operators of hypergeometric type

Starting from Rodrigues formula we present a general construction of raising and lowering operators for orthogonal polynomials of continuous and discrete variable on uniform lattice. In order to have these operators mutually adjoint we introduce orthonormal functions with respect to the scalar product of unit weight. Using the Infeld-Hull factorization method, we generate from the raising and lowering operators the second order self-adjoint differential/difference operator of hypergeometric type.Comment: LaTeX, 24 pages, iopart style (late submission

The double torus as a 2D cosmos: groups, geometry and closed geodesics

The double torus provides a relativistic model for a closed 2D cosmos with topology of genus 2 and constant negative curvature. Its unfolding into an octagon extends to an octagonal tessellation of its universal covering, the hyperbolic space H^2. The tessellation is analysed with tools from hyperbolic crystallography. Actions on H^2 of groups/subgroups are identified for SU(1, 1), for a hyperbolic Coxeter group acting also on SU(1, 1), and for the homotopy group \Phi_2 whose extension is normal in the Coxeter group. Closed geodesics arise from links on H^2 between octagon centres. The direction and length of the shortest closed geodesics is computed.Comment: Latex, 27 pages, 5 figures (late submission to arxiv.org

Creating pseudo Kondo-resonances by field-induced diffusion of atomic hydrogen

In low temperature scanning tunneling microscopy (STM) experiments a cerium adatom on Ag(100) possesses two discrete states with significantly different apparent heights. These atomic switches also exhibit a Kondo-like feature in spectroscopy experiments. By extensive theoretical simulations we find that this behavior is due to diffusion of hydrogen from the surface onto the Ce adatom in the presence of the STM tip field. The cerium adatom possesses vibrational modes of very low energy (3-4meV) and very high efficiency (> 20%), which are due to the large changes of Ce-states in the presence of hydrogen. The atomic vibrations lead to a Kondo-like feature at very low bias voltages. We predict that the same low-frequency/high-efficiency modes can also be observed at lanthanum adatoms.Comment: five pages and four figure

Surface embedding, topology and dualization for spin networks

Spin networks are graphs derived from 3nj symbols of angular momentum. The surface embedding, the topology and dualization of these networks are considered. Embeddings into compact surfaces include the orientable sphere S^2 and the torus T, and the not orientable projective space P^2 and Klein's bottle K. Two families of 3nj graphs admit embeddings of minimal genus into S^2 and P^2. Their dual 2-skeletons are shown to be triangulations of these surfaces.Comment: LaTeX 17 pages, 6 eps figures (late submission to arxiv.org

Kinematic assessment of subject personification of human body models (THUMS)

The goal of this study was to quantify the effect of improving the geometry of a human body model on the accuracy of the predicted kinematics for 4 post-mortem human subject sled tests. Three modifications to the computational human body model THUMS were carried out to evaluate if subject personification can increase the agreement between predicted and measured kinematics of post-mortem human subjects in full frontal and nearside oblique impacts. The modifications consisted of: adjusting the human body model mass to the actual subject mass, morphing it to the actual anthropometry of each subject and finally adjustment of the model initial position to the measured position in selected post-mortem human subject tests. A quantitative assessment of the agreement between predicted and measured response was carried out by means of CORA analysis by comparing the displacement of selected anatomical landmarks (head CoG, T1 and T8 vertebre and H-Point). For all three scenarios, the more similar the human body model was to the anthropometry and posture of the sled tested post-mortem human subject, the more similar the predictions were to the measured responses of the post-mortem human subject, resulting in higher CORA score

Effects of Including a Penetration Test in Motorcyclist Helmet Standards: Influence on Helmet Stiffness and Impact Performance

Regulation ECE-22.05/06 does not require a helmet penetration test. Penetration testing is controversial since it has been shown that it may cause the helmet to behave in a non-desirable stiff way in real-world crashes. This study aimed to assess the effect of the penetration test in the impact performance of helmets. Twenty full-face motorcycle helmets were penetration tested at multiple locations of the helmet shell. Then, 10 helmets were selected and split into two groups (hard shell and soft shell) depending on the results of the penetration tests. These 10 helmets were then drop tested at front, lateral, and top areas at two different impact speeds (5 m/s and 8.2 m/s) to assess their impact performance against head injuries. The statistical analyses did not show any significant difference between the two groups (hard/soft shell) at 5 m/s. Similar results were observed at 8.2 m/s, except for the top area of the helmet in which the peak linear acceleration was significantly higher for the soft shell group than for the hard shell group (230 ± 12 g vs. 211 ± 11 g; p-value = 0.038). The results of this study suggest that a stiffer shell does not necessarily cause helmets to behave in a stiffer way when striking rigid flat surfaces. These experiments also showed that hard shell helmets can provide better protection at higher impact speeds without damaging helmet performance at lower impact speeds. © 2022 by the authors. Licensee MDPI, Basel, Switzerland

Antihyperon potentials in nuclei via exclusive antiproton-nucleus reactions

The exclusive production of hyperon-antihyperon pairs close to their production threshold in antiproton - nucleus collisions offers a unique and hitherto unexplored opportunity to elucidate the behaviour of antihyperons in nuclei. For the first time we analyse these reactions in a microscopic transport model using the the Gie\ss en Boltzmann-Uehling-Uhlenbeck transport model. The calculation take the delicate interplay between the strong absorption of antihyperons, their rescattering and refraction at the nuclear surface as well as the Fermi motion of the struck nucleon into account. We find a substantial sensitivity of transverse momentum correlations of coincident $\Lambda\overline{\Lambda}$-pairs to the assumed depth of the $\overline{\Lambda}$-potential. Because of the high cross section for this process and the simplicity of the experimental method our results are highly relevant for future activities at the international Facility for Antiproton and Ion Research (FAIR)

Finite-Dimensional Calculus

We discuss topics related to finite-dimensional calculus in the context of finite-dimensional quantum mechanics. The truncated Heisenberg-Weyl algebra is called a TAA algebra after Tekin, Aydin, and Arik who formulated it in terms of orthofermions. It is shown how to use a matrix approach to implement analytic representations of the Heisenberg-Weyl algebra in univariate and multivariate settings. We provide examples for the univariate case. Krawtchouk polynomials are presented in detail, including a review of Krawtchouk polynomials that illustrates some curious properties of the Heisenberg-Weyl algebra, as well as presenting an approach to computing Krawtchouk expansions. From a mathematical perspective, we are providing indications as to how to implement in finite terms Rota's "finite operator calculus".Comment: 26 pages. Added material on Krawtchouk polynomials. Additional references include