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

A cotunneling mechanism for all-electrical Electron Spin Resonance of single adsorbed atoms

The recent development of all-electrical electron spin resonance (ESR) in a scanning tunneling microscope (STM) setup has opened the door to vast applications. Despite the fast growing number of experimental works on STM-ESR, the fundamental principles remains unclear. By using a cotunneling picture, we show that the spin resonance signal can be explained as a time-dependent variation of the tunnel barrier induced by the alternating electric driving field. We demonstrate how this variation translates into the resonant frequency response of the direct current. Our cotunneling theory explains the main experimental findings. Namely, the linear dependence of the Rabi flop rate with the alternating bias amplitude, the absence of resonant response for spin-unpolarized currents, and the weak dependence on the actual atomic species.Comment: 11 pages, 3 figure

Many-body effects in magnetic inelastic electron tunneling spectroscopy

Magnetic inelastic electron tunneling spectroscopy (IETS) shows sharp increases in conductance when a new conductance channel associated to a change in magnetic structure is open. Typically, the magnetic moment carried by an adsorbate can be changed by collision with a tunneling electron; in this process the spin of the electron can flip or not. A previous one-electron theory [Phys. Rev. Lett. {\bf 103}, 176601 (2009)] successfully explained both the conductance thresholds and the magnitude of the conductance variation. The elastic spin flip of conduction electrons by a magnetic impurity leads to the well known Kondo effect. In the present work, we compare the theoretical predictions for inelastic magnetic tunneling obtained with a one-electron approach and with a many-body theory including Kondo-like phenomena. We apply our theories to a singlet-triplet transition model system that contains most of the characteristics revealed in magnetic IETS. We use two self-consistent treatments (non-crossing approximation and self-consistent ladder approximation). We show that, although the one-electron limit is properly recovered, new intrinsic many-body features appear. In particular, sharp peaks appear close to the inelastic thresholds; these are not localized exactly at thresholds and could influence the determination of magnetic structures from IETS experiments.Analysis of the evolution with temperature reveals that these many-body features involve an energy scale different from that of the usual Kondo peaks. Indeed, the many-body features perdure at temperatures much larger than the one given by the Kondo energy scale of the system.Comment: 10 pages and 6 figure

Specsim: The MIRI Medium Resolution Spectrometer Simulator

MIRI, the Mid-InfraRed Instrument, is one of four instruments being built for the James Webb Space Telescope, and is developed jointly between an EuropeanConsortium and the US. In this paper we present a software data simulator for one of MIRI's four instruments: the Integral Field Unit (IFU) Medium Resolution Spectrometer (MIRI-MRS), the first mid-infrared IFU spectrograph, and one of the first IFUs to be used in a space mission. To give the MIRI community a preview of the properties of the MIRI-MRS data products before the telescope is operational, the Specsim tool has been developed to model, in software, the operation of the spectrometer. Specsim generates synthetic data frames approximating those which will be taken by the instrument in orbit. The program models astronomical sources and generates detector frames using the predicted and measured optical properties of the telescope and MIRI. These frames can then be used to illustrate and inform a range of operational activities, including data calibration strategies and the development and testing of the data reduction software for the MIRI-MRS. Specsim will serve as a means of communication between the many consortium members by providing a way to easily illustrate the performance of the spectrometer under different circumstances, tolerances of components and design scenarios.Comment: 8 pages, 5 figures; A high resolution version is available at http://www.roe.ac.uk/~npfl/Publications/lgw+06.ps.gz (Changed URL of high-res version

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

Analysing inter-relationships among water, governance, human development variables in developing countries

The "Integrated Water Resources Management" principle was formally laid down at the International Conference on Water and Sustainable development in Dublin 1992. One of the main results of this conference is that improving Water and Sanitation Services (WSS), being a complex and interdisciplinary issue, passes through collaboration and coordination of different sectors (environment, health, economic activities, governance, and international cooperation). These sectors influence or are influenced by the access to WSS. The understanding of these interrelations appears as crucial for decision makers in the water sector. In this framework, the Joint Research Centre (JRC) of the European Commission (EC) has developed a new database (WatSan4Dev database) containing 42 indicators (called variables in this paper) from environmental, socio-economic, governance and financial aid flows data in developing countries. This paper describes the development of the WatSan4Dev dataset, the statistical processes needed to improve the data quality, and finally, the analysis to verify the database coherence is presented. Based on 25 relevant variables, the relationships between variables are described and organised into five factors (HDP – Human Development against Poverty, AP – Human Activity Pressure on water resources, WR – Water Resources, ODA – Official Development Aid, CEC – Country Environmental Concern). Linear regression methods are used to identify key variables having influence on water supply and sanitation. First analysis indicates that the informal urbanisation development is an important factor negatively influencing the percentage of the population having access to WSS. Health, and in particular children's health, benefits from the improvement of WSS. Irrigation is also enhancing Water Supply service thanks to multi-purpose infrastructure. Five country profiles are also created to deeper understand and synthetize the amount of information gathered. This new classification of countries is useful in identifying countries with a less advanced position and weaknesses to be tackled. The relevance of indicators gathered to represent environmental and water resources state is questioned in the discussion section. The paper concludes with the necessity to increase the reliability of current indicators and calls for further research on specific indicators, in particular on water quality at national scale, in order to better include environmental state in analysis to WSS

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