Pseudo-Unitary Operators and Pseudo-Unitary Quantum Dynamics

We consider pseudo-unitary quantum systems and discuss various properties of pseudo-unitary operators. In particular we prove a characterization theorem for block-diagonalizable pseudo-unitary operators with finite-dimensional diagonal blocks. Furthermore, we show that every pseudo-unitary matrix is the exponential of $i=\sqrt{-1}$ times a pseudo-Hermitian matrix, and determine the structure of the Lie groups consisting of pseudo-unitary matrices. In particular, we present a thorough treatment of $2\times 2$ pseudo-unitary matrices and discuss an example of a quantum system with a $2\times 2$ pseudo-unitary dynamical group. As other applications of our general results we give a proof of the spectral theorem for symplectic transformations of classical mechanics, demonstrate the coincidence of the symplectic group $Sp(2n)$ with the real subgroup of a matrix group that is isomorphic to the pseudo-unitary group U(n,n), and elaborate on an approach to second quantization that makes use of the underlying pseudo-unitary dynamical groups.Comment: Revised and expanded version, includes an application to symplectic transformations and groups, accepted for publication in J. Math. Phy

A proposal for testing Quantum Gravity in the lab

Attempts to formulate a quantum theory of gravitation are collectively known as {\it quantum gravity}. Various approaches to quantum gravity such as string theory and loop quantum gravity, as well as black hole physics and doubly special relativity theories predict a minimum measurable length, or a maximum observable momentum, and related modifications of the Heisenberg Uncertainty Principle to a so-called generalized uncertainty principle (GUP). We have proposed a GUP consistent with string theory, black hole physics and doubly special relativity theories and have showed that this modifies all quantum mechanical Hamiltonians. When applied to an elementary particle, it suggests that the space that confines it must be quantized, and in fact that all measurable lengths are quantized in units of a fundamental length (which can be the Planck length). On the one hand, this may signal the breakdown of the spacetime continuum picture near that scale, and on the other hand, it can predict an upper bound on the quantum gravity parameter in the GUP, from current observations. Furthermore, such fundamental discreteness of space may have observable consequences at length scales much larger than the Planck scale. Because this influences all the quantum Hamiltonians in an universal way, it predicts quantum gravity corrections to various quantum phenomena. Therefore, in the present work we compute these corrections to the Lamb shift, simple harmonic oscillator, Landau levels, and the tunneling current in a scanning tunneling microscope.Comment: v1: 10 pages, REVTeX 4, no figures; v2: minor typos corrected and a reference added. arXiv admin note: has substantial overlap with arXiv:0906.5396 , published in a different journa

Antiferromagnetism of Zn2_2VO(PO4)2_4)_2 and the dilution with Ti4+^{4+}

We report static and dynamic properties of the antiferromagnetic compound Zn$_{2}$(VO)(PO$_{4}$)$_{2}$, and the consequences of non-magnetic Ti$^{4+}$ doping at the V$^{4+}$ site. $^{31}$P nuclear magnetic resonance (NMR) spectra and spin-lattice relaxation rate ($1/T_1$) consistently show the formation of the long-range antiferromagnetic order below $T_N= 3.8-3.9$\,K. The critical exponent $\beta=0.33 \pm 0.02$ estimated from the temperature dependence of the sublattice magnetization measured by $^{31}$P NMR at 9.4\,MHz is consistent with universality classes of three-dimensional spin models. The isotropic and axial hyperfine couplings between the $^{31}$P nuclei and V$^{4+}$ spins are $A_{\rm hf}^{\rm iso} = (9221 \pm 100)$ Oe/$\mu_{\rm B}$ and $A_{\rm hf}^{\rm ax} = (1010 \pm 50)$ Oe/$\mu_{\rm B}$, respectively. Magnetic susceptibility data above 6.5\,K and heat capacity data above 4.5\,K are well described by quantum Monte-Carlo simulations for the Heisenberg model on the square lattice with $J\simeq 7.7$\,K. This value of $J$ is consistent with the values obtained from the NMR shift, $1/T_1$ and electron spin resonance (ESR) intensity analysis. Doping Zn$_2$VO(PO$_4)_2$ with non-magnetic Ti$^{4+}$ leads to a marginal increase in the $J$ value and the overall dilution of the spin lattice. In contrast to the recent \textit{ab initio} results, we find neither evidence for the monoclinic structural distortion nor signatures of the magnetic one-dimensionality for doped samples with up to 15\% of Ti$^{4+}$. The N\'eel temperature $T_{\rm N}$ decreases linearly with increasing the amount of the non-magnetic dopant.Comment: 13 pages, 12 figures, 2 table

Cytoadherence and virulence - the case of Plasmodium knowlesi malaria.

BACKGROUND: Cytoadherence of infected red blood cells to brain endothelium is causally implicated in malarial coma, one of the severe manifestations of falciparum malaria. Cytoadherence is mediated by specific binding of variant parasite antigens, expressed on the surface of infected erythrocytes, to endothelial receptors including, ICAM-1, VCAM and CD36. In fatal cases of severe falciparum malaria with coma, blood vessels in the brain are characteristically congested with infected erythrocytes. Brain sections from a fatal case of knowlesi malaria, but without coma, were similarly congested with infected erythrocytes. The objective of this study was to determine the binding phenotype of Plasmodium knowlesi infected human erythrocytes to recombinant human ICAM-1, VCAM and CD36. METHODS: Five patients with PCR-confirmed P. knowlesi malaria were recruited into the study with consent between April and August 2010. Pre-treatment venous blood was washed and cultured ex vivo to increase the proportion of schizont-infected erythrocytes. Cultured blood was seeded into Petri dishes with triplicate areas coated with ICAM-1, VCAM and CD36. Following incubation at 37°C for one hour the dishes were washed and the number of infected erythrocytes bound/mm2 to PBS control areas and to recombinant human ICAM-1 VCAM and CD36 coated areas were recorded. Each assay was performed in duplicate. Assay performance was monitored with the Plasmodium falciparum clone HB3. RESULTS: Blood samples were cultured ex vivo for up to 14.5 h (mean 11.3 ± 1.9 h) to increase the relative proportion of mature trophozoite and schizont-infected red blood cells to at least 50% (mean 65.8 ± 17.51%). Three (60%) isolates bound significantly to ICAM-1 and VCAM, one (20%) isolate bound to VCAM and none of the five bound significantly to CD36. CONCLUSIONS: Plasmodium knowlesi infected erythrocytes from human subjects bind in a specific but variable manner to the inducible endothelial receptors ICAM-1 and VCAM. Binding to the constitutively-expressed endothelial receptor CD36 was not detected. Further work will be required to define the pathological consequences of these interactions

Spin dependent structure function g_1 at low x and low Q^2

Theoretical description of the spin dependent structure function g_1(x,Q^2) in the region of low values of x and Q^2 is presented. It contains the Vector Meson Dominance contribution and the QCD improved parton model suitably extended to the low Q^2 domain. Theoretical predictions are compared with the recent experimental data in the low x, low Q^2 region

Calculation of clearances in twin screw compressors

Clearances between rotating and stationary parts in a screw compressor are set to ensure the efficient operation and allow for thermal deformation without unwanted contacts. The change in clearances is caused by both pressure and temperature changes within the machine. If clearances are too large, the increased leakage flows will reduce efficiency. However, if the nominal clearances are too small, contacts between the rotating and stationary parts can occur as a consequence of rotor and casing deformations. In order to determine the operational clearances, a numerical analysis of deformation of screw compressor rotors and casing has to be performed. This paper discusses how the temperature of rotor and casing surfaces calculated from the one-dimensional chamber model in the SCORG could be used as a boundary conditions for a steady state thermal and structural analysis of a screw compressor solid parts. Deformations of rotors and casing under temperature load were calculated using a commercial Finite Element Analysis code ANSYS. Operational clearance are estimated from these deformations and some recommendations for further work are proposed

Contribution à l’évaluation de la contamination par les métaux lourds de trois espèces de poissons, des sédiments et des eaux du Lac Tchad

Les fleuves Logone et Chari qui se jettent dans le Lac Tchad, sont exposés à toute forme de pollution. Le but de ce travail est d’évaluer la  contamination par les métaux lourds des eaux, des sédiments et des poissons du Lac Tchad. Trois espèces de poissons: Tilapia nilotica, Lates niloticus et Arius latiscutatus ont été obtenues au Lac Tchad et  transportées sous glace au laboratoire. Le Cd, le Pb et le Cr ont été dosés dans la tête, le foie, la chair et les os de ces poissons, dans les sédiments et l’eau au spectrophotomètre d’absorption atomique. Le Cd et le Pb n’étaient pas détectés dans les eaux et les sédiments. En comparant nos résultats obtenus dans la chair des poissons, à la grille de qualité de Mersch, la pollution des eaux du Lac Tchad va d’une situation intermédiaire (Cd) à une pollution importante (Cr). Les sédiments étaient plus  contaminés que les eaux. Toutes ces valeurs sont au-delà des normes existantes. L’analyse des variances (ANOVA) inter espèces, au seuil de 95% entre les organes, montre qu’il y a une corrélation positive (r = 0,74) et très significative (p = 0,02) entre la chair et les os des différentes espèces.Mots clés : Lac Tchad, métaux lourds, poissons, bioaccumulation

Entangled Quantum State Discrimination using Pseudo-Hermitian System

We demonstrate how to discriminate two non-orthogonal, entangled quantum state which are slightly different from each other by using pseudo-Hermitian system. The positive definite metric operator which makes the pseudo-Hermitian systems fully consistent quantum theory is used for such a state discrimination. We further show that non-orthogonal states can evolve through a suitably constructed pseudo-Hermitian Hamiltonian to orthogonal states. Such evolution ceases at exceptional points of the pseudo-Hermitian system.Comment: Latex, 9 pages, 1 figur

Isospectrality of conventional and new extended potentials, second-order supersymmetry and role of PT symmetry

We develop a systematic approach to construct novel completely solvable rational potentials. Second-order supersymmetric quantum mechanics dictates the latter to be isospectral to some well-studied quantum systems. $\cal PT$ symmetry may facilitate reconciling our approach to the requirement that the rationally-extended potentials be singularity free. Some examples are shown.Comment: 13 pages, no figure, some additions to introduction and conclusion, 4 more references; to be published in Special issue of Pramana - J. Phy