Trions in a periodic potential

The group-theoretical classification of trion states is presented. It is based on considerations of products of irreducible representations of the 2D translation group. For a given BvK period N degeneracy of obtained states is N^2. Trions consist of two identical particles so the symmetrization of states with respect to particles transposition is considered. Completely antisymmetric states can be constructed by introducing antisymmetric spin functions. Two symmetry adapted bases are considered. The third possibility is postponed for the further investigations.Comment: revtex, 5 p., sub. to Physica

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

Understanding Selectivity of Mesoporous Silica-Grafted Diglycolamide-Type Ligands in the Solid-Phase Extraction of Rare Earths

Rare earth elements (REEs) and their compounds are essential for rapidly developing modern technologies. These materials are especially critical in the area of green/sustainable energy; however, only very high-purity fractions are appropriate for these applications. Yet, achieving efficient REE separation and purification in an economically and environmentally effective way remains a challenge. Moreover, current extraction technologies often generate large amounts of undesirable wastes. In that perspective, the development of selective, reusable, and extremely efficient sorbents is needed. Among numerous ligands used in the liquid-liquid extraction (LLE) process, the diglycolamide-based (DGA) ligands play a leading role. Although these ligands display notable extraction performance in the liquid phase, their extractive chemistry is not widely studied when such ligands are tethered to a solid support. A detailed understanding of the relationship between chemical structure and function (i.e., extraction selectivity) at the molecular level is still missing although it is a key factor for the development of advanced sorbents with tailored selectivity. Herein, a series of functionalized mesoporous silica (KIT-6) solid phases were investigated as sorbents for the selective extraction of REEs. To better understand the extraction behavior of these sorbents, different spectroscopic techniques (solid-state NMR, X-ray photoelectron spectroscopy, XPS, and Fourier transform infrared spectroscopy, FT-IR) were implemented. The obtained spectroscopic results provide useful insights into the chemical environment and reactivity of the chelating ligand anchored on the KIT-6 support. Furthermore, it can be suggested that depending on the extracted metal and/or structure of the ligand and its attachment to KIT-6, different functional groups (i.e., C= O, N-H, or silanols) act as the main adsorption centers and preferentially capture targeted elements, which in turn may be associated with the different selectivity of the synthesized sorbents. Thus, by determining how metals interact with different supports, we aim to better understand the solid-phase extraction process of hybrid (organo)silica sorbents and design better extraction materials

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

Impact of Unexpected Events, Shocking News and Rumours on Foreign Exchange Market Dynamics

We analyze the dynamical response of the world's financial community to various types of unexpected events, including the 9/11 terrorist attacks as they unfolded on a minute-by-minute basis. We find that there are various 'species' of news, characterized by how quickly the news get absorbed, how much meaning and importance is assigned to it by the community, and what subsequent actions are then taken. For example, the response to the unfolding events of 9/11 shows a gradual collective understanding of what was happening, rather than an immediate realization. For news items which are not simple economic statements, and hence whose implications are not immediately obvious, we uncover periods of collective discovery during which collective opinions seem to oscillate in a remarkably synchronized way. In the case of a rumour, our findings also provide a concrete example of contagion in inter-connected communities. Practical applications of this work include the possibility of producing selective newsfeeds for specific communities, based on their likely impact

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

Diazepam and its metabolites in the mothers' and newborns' hair as a biomarker of prenatal exposure

Pregnant women are exposed to benzodiazepines for therapeutic purposes during gestation. The goal of this study was to evaluate prenatal exposure to benzodiazepines. Time of exposure during course of pregnancy is a significant aspect of fetal exposure to drugs. Benzodiazepine concentration assay in hair of mothers and newborns exposed prenatally to these drugs was performed in the studies. Development, validation and evaluation of benzodiazepine determination method in mothers and their newborns enables assessment of health risks for the child and implementation of adequate therapeutic procedures. We used A LC-ESI-MS/MS method that allowed determination of diazepam (the main benzodiazepine used by pregnant women was diazepam) and its metabolites (nordazepam, oxazepam) in hair of mothers and newborns. LOQ 10 pg/mg of hair was used in the study. Results: concentration of nordazepam was higher than parent drug (diazepam) and higher in newborns’ hair when compared to mothers’. The mean concentrations of diazepam in mothers’ hair were 31.6±36.0 and 34.1±42.4 pg/mg in the second and third trimester of pregnancy respectively. The mean concentration of diazepam in newborns’ hair was higher and reached levels of 53.3±36.5 pg/mg. The mean concentration of nordazepam in the mothers’ hair corresponding to the second and third trimester was 52.9±48.1 and 89.9±122.8 pg/mg, respectively. Nordazepam in the newborns’ hair was detected at the mean level of 108.1±144.2 pg/mg. It was concluded that diazepam and nordazepam are permanently incorporated into the hair structure. Presence of diazepam and its metabolites in newborn’s hair confirms that these benzodiazepines permeate placental barrier. Segmental analysis of mothers’ hair enabled the assessment of drug administration time. Diazepam and its metabolites determined in hair of newborns may serve as biomarkers of prenatal exposure to these drugs. The performed LC-MS/MS analysis was accurate enough to determine even low concentrations of benzodiazepines, at the level of few pg/mg of hair. Levels of diazepam detected in hair of newborns were higher than levels determined in mothers. This may confirm the fact, that fetus’s ability to metabolize diazepam is scarce. Nordazepam was found in higher concentrations in hair of newborns than in hair of mothers, which may suggest that it is cumulated in child’s organism. Other metabolites of diazepam - oxazepam and temazepam - were detected in very few cases, in low concentrations

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

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