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

An extension of Fourier analysis for the n-torus in the magnetic field and its application to spectral analysis of the magnetic Laplacian

We solved the Schr{\"o}dinger equation for a particle in a uniform magnetic field in the n-dimensional torus. We obtained a complete set of solutions for a broad class of problems; the torus T^n = R^n / {\Lambda} is defined as a quotient of the Euclidean space R^n by an arbitrary n-dimensional lattice {\Lambda}. The lattice is not necessary either cubic or rectangular. The magnetic field is also arbitrary. However, we restrict ourselves within potential-free problems; the Schr{\"o}dinger operator is assumed to be the Laplace operator defined with the covariant derivative. We defined an algebra that characterizes the symmetry of the Laplacian and named it the magnetic algebra. We proved that the space of functions on which the Laplacian acts is an irreducible representation space of the magnetic algebra. In this sense the magnetic algebra completely characterizes the quantum mechanics in the magnetic torus. We developed a new method for Fourier analysis for the magnetic torus and used it to solve the eigenvalue problem of the Laplacian. All the eigenfunctions are given in explicit forms.Comment: 32 pages, LaTeX, minor corrections are mad

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

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

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

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

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

Early hematopoietic chimerism monitoring and molecular engraftment characteristic by STR-PCR method in patients after alloHSCT

Allogeniczna transplantacja komórek hematopoetycznych jest jednym ze sposobów leczenia nowotworowych i nienowotworowych schorzeń hematologicznych. Po przeszczepieniu komórki hematopoetyczne dawcy osiedlają się w niszach szpikowych biorcy, co skutkuje powstaniem prawidłowego układu krwiotwórczego i immunologicznego o genotypie dawcy - całkowity chimeryzm dawcy. Wszczepienie molekularne (ME) poprzedza wystąpienie wszczepienia hematologicznego. Wczesna ocena chimeryzmu może mieć istotne znaczenie dla dalszego przebiegu procesu przyjmowania się przeszczepienia i warunkuje możliwość podjęcia wczesnej interwencji leczniczej.Do badania włączono 38 pacjentów, u których wykonano 43 allogeniczne transplantacje (alloHSCT). Przyjmowanie się przeszczepu śledzono we krwi obwodowej od 2. do 14. doby po transplantacji, następnie w 21. i 28. dobie. W 30. dobie poziom chimeryzmu oznaczano we krwi obwodowej i w szpiku kostnym. Chimeryzm hematopoetyczny oceniano przy zastosowaniu metody molekularnej STR-PCR.Wykazano, że zmiany poziomu chimeryzmu we wczesnym okresie po transplantacji w grupie pacjentów poddanych alloSCT (alloHSCT po-przedzona kondycjonowaniem mieloablacyjnym) przebiegają zgodnie z zależnością liniową (R2=0,996), natomiast w grupie pacjentów poddanych alloNMSCT (alloHSCT poprzedzona kondycjonowaniem niemie-loablacyjnym) są zgodne z zależnością logarytmiczną (R2=0,959). Poziom chimeryzmu hematopoetycznego jest wyższy w grupie pacjentów poddanych alloSCT, w 2. dobie różnicę tę cechuje znamienność statystyczna (p=0,0048).Wszczepienie molekularne poprzedza wystąpienie wszczepienia hematologicznego (pacjenci poddani alloSCT p=1,44×10−12, pacjenci pod-dani alloNMSCT p=2,12×10−6).W grupach pacjentów poddanych alloSCT i alloHSCT, którzy otrzymali więcej niż 3×106 komórek CD34+/kg masy data różnica w czasie wystąpienia ME w porównaniu z grupą chorych, którzy otrzymali mniej niż 3×106 komórek CD34+/kg, była znamienna statystycznie (alloSCT p=0,0013, alloHSCT p = 0,021).Allogeneic hematopoietic stem cell transplantation (alloHSCT) is a curative treatment for proportion of patients suffering from malignant and non-malignant hematological disorders. Successful transplantation is a process that requires the engraftment of pluripotent hematopoietic stem cells which can re-establish normal hemopoesis and immune system. Distinguishing between donor and host origin of bone marrow and blood cells is crucial for monitoring of engraftment process. One of the most useful tools for engraftment monitoring is the assessment of hematopoietic chimerism after alloSCT that describes the percentage of donor hematopoietic in a transplant recipient.Thirty eight adult patients after alloHSCT were included into the study. In total 43 allogeneic stem cell transplantations were performed. Hematopoietic chimerism was assessed by STR-PCR technique. The analysis of early chimerism were performed starting from 2nd to 14th day on every 2 days than to 28 days weekly and on day +30 after alloHSCT.Early hematopoietic chimerism assessment demonstrated that the kinetics of chimerism in patients after alloSCT was compatible with linear trend (R2=0.996) and in patients after alloNMSCT was compatible with logarithmic trend (R2=0.959). The hematopoietic chimerism level was higher in alloSCT on day 2 the difference was statistically significant (p=0.0048).Molecular engraftment preceded hematological engraftment in patients after either myeloablative or non-myeloablative conditioning regiments (alloSCT patients p=1.44×10−12, alloNMSCT p=2.12×10−6).Earlier ME was observed in patients after alloHSCT and alloSCT who received more than 3×106 CD34+ cells/kg (alloSCT p=0.0013, alloHSCT p=0.021). The difference was statistically significant

Implementation of U.K. Earth system models for CMIP6

We describe the scientific and technical implementation of two models for a core set of experiments contributing to the sixth phase of the Coupled Model Intercomparison Project (CMIP6). The models used are the physical atmosphere-land-ocean-sea ice model HadGEM3-GC3.1 and the Earth system model UKESM1 which adds a carbon-nitrogen cycle and atmospheric chemistry to HadGEM3-GC3.1. The model results are constrained by the external boundary conditions (forcing data) and initial conditions.We outline the scientific rationale and assumptions made in specifying these. Notable details of the implementation include an ozone redistribution scheme for prescribed ozone simulations (HadGEM3-GC3.1) to avoid inconsistencies with the model's thermal tropopause, and land use change in dynamic vegetation simulations (UKESM1) whose influence will be subject to potential biases in the simulation of background natural vegetation.We discuss the implications of these decisions for interpretation of the simulation results. These simulations are expensive in terms of human and CPU resources and will underpin many further experiments; we describe some of the technical steps taken to ensure their scientific robustness and reproducibility