The expressions for the 2nd-order mixed partial derivatives of Slater-Koster matrix elements at spherical coordinate singularities

In a recent publication it has been shown how to generate derivatives with respect to atom coordinates of Slater-Koster matrix elements for the tight binding (TB) modelling of a system. For the special case of a mixed second partial derivative at coordinate singularities only the results were stated in that publication. In this work, the derivation of these results is given in detail. Though it may seem rather `technical' and only applicable to a very special case, atomic configurations where the connecting vector between the two atoms involved in a two-centre matrix element is aligned along the z-axis (in the usual approach) require results for precisely this case. The expressions derived in this work have been implemented in the DINAMO code.Comment: 9 pages, no figure

Efficient matter-wave lensing of ultracold atomic mixtures

Mixtures of ultracold quantum gases are at the heart of high-precision quantum tests of the weak equivalence principle, where extremely low expansion rates have to be reached with matter-wave lensing techniques. We propose to simplify this challenging atom-source preparation by employing magic laser wavelengths for the optical lensing potentials which guarantee that all atomic species follow identical trajectories and experience common expansion dynamics. In this way, the relative shape of the mixture is conserved during the entire evolution while cutting in half the number of required lensing pulses compared to standard approaches.Comment: 9 pages, 3 figure

Automatic Generation of Matrix Element Derivatives for Tight Binding Models

Tight binding (TB) models are one approach to the quantum mechanical many particle problem. An important role in TB models is played by hopping and overlap matrix elements between the orbitals on two atoms, which of course depend on the relative positions of the atoms involved. This dependence can be expressed with the help of Slater-Koster parameters, which are usually taken from tables. Recently, a way to generate these tables automatically was published. If TB approaches are applied to simulations of the dynamics of a system, also derivatives of matrix elements can appear. In this work we give general expressions for first and second derivatives of such matrix elements. Implemented in a computer program they obviate the need to type all the required derivatives of all occuring matrix elements by hand.Comment: 11 pages, 2 figure

The interface of gravity and quantum mechanics illuminated by Wigner phase space

We provide an introduction into the formulation of non-relativistic quantum mechanics using the Wigner phase-space distribution function and apply this concept to two physical situations at the interface of quantum theory and general relativity: (i) the motion of an ensemble of cold atoms relevant to tests of the weak equivalence principle, and (ii) the Kasevich-Chu interferometer. In order to lay the foundations for this analysis we first present a representation-free description of the Kasevich-Chu interferometer based on unitary operators.Comment: 69 pages, 6 figures, minor changes to match the published version. The original publication is available at http://en.sif.it/books/series/proceedings_fermi or http://ebooks.iospress.nl/volumearticle/3809

Cavity Disinfection With a 445 nm Diode Laser Within the Scope of Restorative Therapy – A Pilot Study

Introduction: Cavity disinfection is necessary to prevent a progressive infection of the crown dentin and pulp. Increasing intolerance and resistance to antiseptics and antibiotics as well as the controversy over the effects of those on the dental hard tissue and composite have prompted the investigation of alternative treatment options. The objective of this pilot study is to evaluate the antibacterial potential of a diode laser with a wavelength of 445 nm in the cavity preparation using the bacterium Streptococcus salivarius associated with caries in conjunction with the characteristics and influences of dentin on light transmission.Methods: The bactericidal effect of the laser irradiation was determined in culture experiments by using caries-free human dentin samples on bacteria-inoculated agar. For this, dentin discs (horizontally cut coronal dentin) of 500 μm and 1000 μm thicknesses were produced and irradiated with the laser with irradiation parameters of 0.7-1 W in a cw-mode and exposure times of between 5-30 s. Based on the different sample thicknesses, the penetration depth effect of the irradiation was ascertained after the subsequent incubation of the bacteria-inoculated agar. Additional influential parameters on the irradiation transmission were investigated, including surface moisture, tooth color as well as the presence of a smear layer on the dentin surface.Results: The optical transmission values of the laser radiation for dentin were significantly dependent on the sample thickness (P = 0.006) as well as its moisture content (P = 0.013) and were independent of the presence of a smear layer. There was a 40% reduction in bacteria after the radiography of the 500-μm-thick dentin samples, which was shown as the lowest laser dose (443 J/cm2).Conclusion: These findings indicate that the diode laser with light emission at a wavelength of 445 nm is interesting for the supportive cavity disinfection within the scope of caries therapy and show potential for clinical applications

Efficient atomic lensing of quantum gas mixtures

Mixtures of ultracold quantum gases are at the heart of currently planned high-precision quantum tests of the weak equivalence principle, where dual-species Bose-Einstein condensates are probed with atom interferometry techniques. An important challenge for such experiments is to reach very low expansion velocities by means of time-dependent potentials acting as matter-wave lenses while ensuring the co-location of the two atomic species and matching their expansion rates during the whole free evolution. To achieve the required control, one lensing pulse is needed for each independent spatial direction and atomic species, which makes a full 3D implementation rather impractical. Here we propose to overcome these challenges by taking advantage of special magic wavelengths for optical dipole traps where the ratio of the optical potentials is given by the ratio of the masses of the different species. In this case the center-of-mass dynamics is identical for all species, resulting in a perfect co-location of the mixture even in an Earth-based laboratory. Most importantly, optical dipole traps with such a magic laser wavelength give riseto a common expansion dynamics for both species and therefore guarantee that the relative shape of the mixture is conserved during the entire evolution, including when the lensing potentials are applied. Hence, our approach enables an efficient collimation of mixtures of ultracold atoms in order to reach the very low expansion rates that are necessary for highprecision measurements while cutting in half the number of required lensing pulses compared to standard approaches

Opposites Attract: An Approach to Collaborative Supply Chain Management between Semiconductor and Automotive Companies

This article illustrates the differences between the semiconductor and the automotive industry and the subsequent challenges to their common supply chain. The weak points at the interfaces between the two supply chains will systematically be identified and assessed. Based on this analysis, a toolkit for collaborative supply chain planning and execution between the automotive and the semiconductor industry is presented. A fit/gap analysis assesses the measures and their potential to solve the supply chain challenges in a systematic manner. The model is built upon existing supply chain management frameworks and defines a set of specific optimization measures for the problem at hand. These are designed to ensure a better alignment of planning and control processes between the automotive and the semiconductor industry

The space atom laser: An isotropic source for ultra-cold atoms in microgravity

Atom laser experiments with Bose-Einstein condensates (BECs) performed in ground-based laboratories feature a coherent and directed beam of atoms which is accelerated by gravity. In microgravity the situation is fundamentally different because the dynamics is entirely determined by the repulsive interaction between the atoms and not by the gravitational force. As a result, the output of a space atom laser is a spherical wave slowly expanding away from the initial BEC. We present a thorough theoretical study of this new source of matter waves based on rf outcoupling which exhibits an isotropic distribution both in position and momentum even for an initially anisotropic trap. The unique geometry of such a freely expanding, shell-shaped BEC offers new possibilities for matter waves in microgravity and is complementary to other matter-wave sources prepared by delta-kick collimation or adiabatic expansion. Our work paves the way for the upcoming experimental realization of a space atom laser making use of NASA's Cold Atom Laboratory on the International Space Station