Pairs of Bloch electrons and magnetic translation groups

A product of irreducible representations of magnetic translation group is considered. It leads to irreducible representations which were previously rejected as nonphysical. A very simple example indicates a possible application of these representations. In particular, they are important in descriptions of pairs of electrons in a magnetic field and a periodic potential. The periodicity of some properties with respect to the charge of a particle is briefly discussed.Comment: 4 pages, RevTex. Latex2.09, amsfont

Spatial clustering of interacting bugs: Levy flights versus Gaussian jumps

A biological competition model where the individuals of the same species perform a two-dimensional Markovian continuous-time random walk and undergo reproduction and death is studied. The competition is introduced through the assumption that the reproduction rate depends on the crowding in the neighborhood. The spatial dynamics corresponds either to normal diffusion characterized by Gaussian jumps or to superdiffusion characterized by L\'evy flights. It is observed that in both cases periodic patterns occur for appropriate parameters of the model, indicating that the general macroscopic collective behavior of the system is more strongly influenced by the competition for the resources than by the type of spatial dynamics. However, some differences arise that are discussed.Comment: This version incorporates in the text the correction published as an Erratum in Europhysics Letters (EPL) 95, 69902 (2011) [doi: 10.1209/0295-5075/95/69902

The usefulness of SPECT/CT in characterization of skeletal and soft tissue lesions — report of two cases

SPECT/CT imaging provides detailed information on the radiotracer distribution and enables simultaneous lesion morphology evaluation. This hybrid imaging delivers complementary information about patient’s disease. We present two cases in which SPECT/CT imaging and cooperation between the nuclear medicine physician and radiologist quickly clarified the diagnosis, sparing patient unnecessary diagnostic procedures or treatment

Spin Polaron Effective Magnetic Model for La_{0.5}Ca_{0.5}MnO_3

The conventional paradigm of charge order for La_{1-x}Ca_xMnO_3 for x=0.5 has been challenged recently by a Zener polaron picture emerging from experiments and theoretical calculations. The effective low energy Hamiltonian for the magnetic degrees of freedom has been found to be a cubic Heisenberg model, with ferromagnetic nearest neighbor and frustrating antiferromagnetic next nearest neighbor interactions in the planes, and antiferromagnetic interaction between planes. With linear spin wave theory and diagonalization of small clusters up to 27 sites we find that the behavior of the model interpolates between the A and CE-type magnetic structures when a frustrating intraplanar interaction is tuned. The values of the interactions calculated by ab initio methods indicate a possible non-bipartite picture of polaron ordering differing from the conventional one.Comment: 21 pages and 8 figures (included), Late

Neel probability and spin correlations in some nonmagnetic and nondegenerate states of hexanuclear antiferromagnetic ring Fe6: Application of algebraic combinatorics to finite Heisenberg spin systems

The spin correlations \omega^z_r, r=1,2,3, and the probability p_N$ of finding a system in the Neel state for the antiferromagnetic ring Fe(III)6 (the so-called `small ferric wheel') are calculated. States with magnetization M=0, total spin 0<=S<=15 and labeled by two (out of four) one-dimensional irreducible representations (irreps) of the point symmetry group D_6 are taken into account. This choice follows from importance of these irreps in analyzing low-lying states in each S-multiplet. Taking into account the Clebsch--Gordan coefficients for coupling total spins of sublattices (SA=SB=15/2) the global Neel probability p*_N can be determined. Dependencies of these quantities on state energy (per bond and in the units of exchange integral J) and the total spin S are analyzed. Providing we have determined p_N(S) etc. for other antiferromagnetic rings (Fe10, for instance) we could try to approximate results for the largest synthesized ferric wheel Fe18. Since thermodynamic properties of Fe6 have been investigated recently, in the present considerations they are not discussed, but only used to verify obtained values of eigenenergies. Numerical results re calculated with high precision using two main tools: (i) thorough analysis of symmetry properties including methods of algebraic combinatorics and (ii) multiple precision arithmetic library GMP. The system considered yields more than 45 thousands basic states (the so-called Ising configurations), but application of the method proposed reduces this problem to 20-dimensional eigenproblem for the ground state (S=0). The largest eigenproblem has to be solved for S=4; its dimension is 60. These two facts (high precision and small resultant eigenproblems) confirm efficiency and usefulness of such an approach, so it is briefly discussed here.Comment: 13 pages, 7 figs, 5 tabs, revtex

Understanding misuse of partially automated vehicles – a discussion of NTSB’s findings of the 2018 Mountain View Tesla Crash

This document discusses a fatal crash from March 23, 2018 involving a Tesla Model X using the partially automated 'Autopilot' function. It provides a critique of the NTSB's report and examines the findings from a human factors perspective to contribute towards an enhanced understanding of the circumstances related to this crash. It concludes with areas for open discussion, recommendations for future investigation and five findings of worthwhile of further consideration. • We question whether 'driver distraction' is an appropriate classification for a "probable cause" of the crash. • We disagree that "familiarization with the vehicle" was not a contributing factor related to this crash. • We question the conclusion that driver qualification was not a contributing factor related to this crash. • We highlight the need for regulatory bodies to ensure effective driver state monitoring and urge for regulation on minimum requirements for driver state monitoring in partially automated vehicles. • We highlight the importance of human-machine interface design in a human-machine shared system and urge for regulation on minimum requirements of such systems within partially automated vehicles. And in doing so we highlight the importance for a human factors perspective of such events

Magnetic translation groups in an n-dimensional torus

A charged particle in a uniform magnetic field in a two-dimensional torus has a discrete noncommutative translation symmetry instead of a continuous commutative translation symmetry. We study topology and symmetry of a particle in a magnetic field in a torus of arbitrary dimensions. The magnetic translation group (MTG) is defined as a group of translations that leave the gauge field invariant. We show that the MTG on an n-dimensional torus is isomorphic to a central extension of a cyclic group Z_{nu_1} x ... x Z_{nu_{2l}} x T^m by U(1) with 2l+m=n. We construct and classify irreducible unitary representations of the MTG on a three-torus and apply the representation theory to three examples. We shortly describe a representation theory for a general n-torus. The MTG on an n-torus can be regarded as a generalization of the so-called noncommutative torus.Comment: 29 pages, LaTeX2e, title changed, re-organized, to be published in Journal of Mathematical Physic

Geometric entropy, area, and strong subadditivity

The trace over the degrees of freedom located in a subset of the space transforms the vacuum state into a density matrix with non zero entropy. This geometric entropy is believed to be deeply related to the entropy of black holes. Indeed, previous calculations in the context of quantum field theory, where the result is actually ultraviolet divergent, have shown that the geometric entropy is proportional to the area for a very special type of subsets. In this work we show that the area law follows in general from simple considerations based on quantum mechanics and relativity. An essential ingredient of our approach is the strong subadditive property of the quantum mechanical entropy.Comment: Published versio

HIRDES - The High-Resolution Double-Echelle Spectrograph for the World Space Observatory Ultraviolet (WSO/UV)

The World Space Observatory Ultraviolet (WSO/UV) is a multi-national project grown out of the needs of the astronomical community to have future access to the UV range. WSO/UV consists of a single UV telescope with a primary mirror of 1.7m diameter feeding the UV spectrometer and UV imagers. The spectrometer comprises three different spectrographs, two high-resolution echelle spectrographs (the High-Resolution Double-Echelle Spectrograph, HIRDES) and a low-dispersion long-slit instrument. Within HIRDES the 102-310nm spectral band is split to feed two echelle spectrographs covering the UV range 174-310nm and the vacuum-UV range 102-176nm with high spectral resolution (R>50,000). The technical concept is based on the heritage of two previous ORFEUS SPAS missions. The phase-B1 development activities are described in this paper considering performance aspects, design drivers, related trade-offs (mechanical concepts, material selection etc.) and a critical functional and environmental test verification approach. The current state of other WSO/UV scientific instruments (imagers) is also described.Comment: Accepted for publication in Advances in Space Researc

The WSO, a world-class observatory for the ultraviolet

The World Space Observatory is an unconventional space project proceeding via distributed studies. The present design, verified for feasibilty, consists of a 1.7-meter telescope operating at the second Largangian point of the Earth-Sun system. The focal plane instruments consist of three UV spectrometers covering the spectral band from Lyman alpha to the atmospheric cutoff with R~55,000 and offering long-slit capability over the same band with R~1,000. In addition, a number of UV and optical imagers view adjacent fields to that sampled by the spectrometers. Their performance compares well with that of HST/ACS and the spectral capabilities of WSO rival those of HST/COS