Algorithmic boundedness-from-below conditions for generic scalar potentials

Checking that a scalar potential is bounded from below (BFB) is an ubiquitous and notoriously difficult task in many models with extended scalar sectors. Exact analytic BFB conditions are known only in simple cases. In this work, we present a novel approach to algorithmically establish the BFB conditions for any polynomial scalar potential. The method relies on elements of multivariate algebra, in particular, on resultants and on the spectral theory of tensors, which is being developed by the mathematical community. We give first a pedagogical introduction to this approach, illustrate it with elementary examples, and then present the working Mathematica implementation publicly available at GitHub. Due to the rapidly increasing complexity of the problem, we have not yet produced ready-to-use analytical BFB conditions for new multi-scalar cases. But we are confident that the present implementation can be dramatically improved and may eventually lead to such results.     

Hyperbolic Octonion Formulation of Gravitational Field Equations

In this paper, the Maxwell-Proca type field equations of linear gravity are formulated in terms of hyperbolic octonions (split octonions). A hyperbolic octonionic gravitational wave equation with massive gravitons and gravitomagnetic monopoles is proposed. The real gravitoelectromagnetic field equations are recovered and written in compact form from an octonionic potential. In the absence of charges, this reduces to the Klein-Gordon equation of motion for the massive graviton. The analogy between massive gravitational theory and electromagnetism is shown in terms of the present formulation.     

Local near field assisted ablation of fused silica

In this contribution we present recent experimental and theoretical results on local near-field assisted laser ablation. Along these lines, we have generated sub-diffraction sized nanostructures on fused silica substrates, exploiting the local near fields of highly ordered triangular gold nanoparticle arrays generated by nanosphere lithography. After preparation, the nanoparticle arrays were irradiated with a single 35 fs long laser pulse with a central wavelength of λ=790 nm. The pulse energy was set to E=3.9 μJ, resulting in a fluence well below the ablation threshold of the fused silica substrates. In addition, 3D electromagnetic simulations using a finite integration technique in time domain have been performed. The simulations demonstrate that indeed the local field in the vicinity of the tips of the triangular nanoparticles overcome the ablation threshold and easily explain the generated nanostructures. Most importantly, the simulations show, that higher order modes contribute to the ablation process. These modes cause ablation along the side edges of the nanoparticles. Finally, we demonstrate, that the optical properties of the triangular nanoparticles, which can be tuned by their morphology, are crucial parameters for the generation of the ablation structures.     

Room‐temperature terahertz emission from ZnSe‐based quantum cascade structures: A simulation study

We identified conditions for room‐temperature operation of terahertz quantum cascade lasers (THz QCLs) where variable barrier heights are used on ZnSe/Zn_1–xMg_x Se material systems. The THz QCL devices are based on three‐level two‐well design schemes. The THz QCL lasers with alternating quantum barriers with different heights were compared with THz QCL laser structures with fixed quantum barrier heights. It is found that the THz QCL device with novel design employing variable barrier heights achieved the terahertz emission of about 1.45 THz at room‐temperature (300 K), and has improved laser performance due to the suppression of thermally activated carrier leakage via higher‐energy parasitic levels. Thus, THz QCL devices employing the design with variable barrier heights may lead to future improvements of the operating temperature and performance of THz QCL lasers. (© 2016 WILEY‐VCH Verlag GmbH &Co. KGaA, Weinheim)     

Hawking Radiation of Scalar and Vector Particles from 5D Myers-Perry Black Holes

In the present paper we explore the Hawking radiation as a quantum tunneling effect from a rotating 5 dimensional Myers-Perry black hole (5D-MPBH) with two independent angular momentum components. First, we investigate the Hawking temperature by considering the tunneling of massive scalar particles and spin-1 vector particles from the 5D-MPBH in the Painlevé coordinates and then in the corotating frames. More specifically, we solve the Klein-Gordon and Proca equations by applying the WKB method and Hamilton-Jacobi equation in both cases. Finally, we recover the Hawking temperature and show that coordinates systems do not affect the Hawking temperature.     

On geometric interpretations of split quaternions

Quaternions are an important tool that provides a convenient and effective mathematical method for representing reflections and rotations in three-dimensional space. A unit timelike split quaternion represents a rotation in the Lorentzian space. In this paper, we give some geometric interpretations of split quaternions for lines and planes in the Minkowski 3-space with the help of mutual pseudo orthogonal planes. We classified mutual planes with respect to the casual character of the normals of the plane as follows; if the normal is timelike, then the mutual plane is isomorphic to the complex plane; if the normal is spacelike, then the plane is isomorphic to the hyperbolic number plane (Lorentzian plane); if the normal is lightlike, then the plane is isomorphic to the dual number plane (Galilean plane).     

Magnetism in hydrogenated YBa2Cu3O7 a comparison of μSR and NMR results

Hydrogenated YBa₂Cu₃O₇ with [H]/cell=2.0 was studied by X-ray diffraction, SR and¹H-NMR. For the first time, the hydride phase (16% larger c-axis) known from thin film experiments was seen in a bulk sample. A comparison of the SR and NMR results shows that the 15 mT site (2 MHz in SR) is the stable position for the proton and muon. The three other muon sites (4 MHz line and two exponentially decaying components) are metastable.     

Calculation of muon level-crossing resonance spectra for Si∶B and Si∶Al

The spin dynamics of muons interacting with acceptor impurity nuclei in silicon is investigated. Using values of electric field gradients obtained from ab-initio calculations, the field dependence of the longitudinal muon polarization is calculated for SiB and SiAl and compared to the contributions from paramagnetic bond-center muonium.     

Theory of adsorption: Ordered monolayers from Na to Cl on Si(001) and Ge(001)

First principles calculations of clean and adsorbate-covered surfaces of Si(001) and Ge(001) are reported. Chemical trends in the adsorption of ordered Na, K, Ge, As, Sb, S, Se and Cl overlayers are discussed. The calculations are based on the local-density approximation and employ non-local, norm-conserving pseudopotentials together with Gaussian orbital basis sets. The semi-infinite geometry of the substrate is properly taken into account by employing our scattering theoretical method. From total-energy minimization calculations we obtain optimal surface reconstructions which show asymmetric dimers for Si(001), Ge(001) and Ge:Si(001). For As:Si(001), Sb:Si(001) and Sb:Ge(001), we find symmetric adatom dimers in the equilibrium geometries. S or Se adlayers are found to be adsorbed in bridge positions forming a (1×1) unit cell with a geometry very close to the configuration of a terminated bulk lattice. Cl atoms adsorb on top of the dangling bonds of symmetric Si dimers residing in the first substrate-surface layer. Our calculations for Na:Si(001) and K:Si(001) confirm valley-bridge site adsorption for half monolayer coverage. For full monolayer alkali-metal coverage, adsorption in pedestal and valley-bridge positions is found to be energetically most favourable. The calculated optimal adsorption configurations are in excellent agreement with a whole body of recent experimental data on surface-structure determination. For these structural models, we obtain electronic surface band structures which agree very good with a wealth of data from angle-resolved photoemission spectroscopy investigations.