$${\mathcal{N}=2}$$ Superconformal Algebra and the Entropy of Calabi–Yau Manifolds

We use the representation theory of \({\mathcal{N}=2}\) superconformal algebra to study the elliptic genera of Calabi–Yau (CY) D-folds. We compute the entropy of CY manifolds from the growth rate of multiplicities of the massive (non-BPS) representations in the decomposition of their elliptic genera. We find that the entropy of CY manifolds of complex dimension D behaves differently depending on whether D is even or odd. When D is odd, CY entropy coincides with the entropy of the corresponding hyperKähler (D ? 3)-folds due to a structural theorem on Jacobi forms. In particular, we find that the Calabi–Yau 3-fold has a vanishing entropy. At D > 3, using our previous results on hyperKähler manifolds, we find \({S_{CY_D}\sim 2\pi \sqrt{\frac{(D-3)^2}{2(D-1)}n}}\). When D is even, we find the behavior of CY entropy behaving as \({S_{CY_D}\sim 2 \pi\sqrt{\frac{D-1}{2}n}}\). These agree with Cardy’s formula at large D.     

On the two-loop $$ \ma thcal{O} $$( αs2) correc tions to the pole mass of the t quark in the MSSM

The paper is devoted to the calculation of two-loop (α _s ²) MSSM corrections to the relation between the pole mass of the t quark and its running mass in the scheme. Firstly, the value of the second-order contribution from large-mass expansion in mt/M _SUSY is studied. Contrary to our expectations, this contribution turned out to be negligible. As a by-product of this calculation, the two-loop anomalous dimension of the running quark mass is obtained in the supersymmetric QCD. Secondly, the influence of the two-loop corrections to the t-quark mass on the predicted superpartner masses is investigated. The text was submitted by the authors in English.     

Canonical Form and Separability of PPT States in C2(×)C2(×)C2(×)CN Composite Quantum Systems

We give a canonical form of PPT states in C2(×)C2(×)C2(×)CN with rank = N. From this canonical form a sufficient separability condition for these states is presented.     

Dual Fluorometric Detection of Fe3+ and Hg2+ Ions in an Aqueous Medium Using Carbon Quantum Dots as a “Turn-off” Fluorescence Sensor

The present study aimed to develop a carbon dots-based fluorescence (FL) sensor that can detect more than one pollutant simultaneously in the same aqueous solution. The carbon dots-based FL sensor has been prepared by employing a facile hydrothermal method using citric acid and ethylenediamine as precursors. The as-synthesized CDs displayed excellent hydrophilicity, good photostability and blue fluorescence under UV light. They have been used as an efficient “turn-off” FL sensor for dual sensing of Fe³⁺ and Hg²⁺ ions in an aqueous medium with high sensitivity and selectivity through a static quenching mechanism. The lowest limit of detection (LOD) for Fe³⁺ and Hg²⁺ ions was found to be 0.406 µM and 0.934 µM, respectively over the concentration range of 0-50 µM. Therefore, the present work provides an effective strategy to monitor the concentration of Fe³⁺ and Hg²⁺ ions simultaneously in an aqueous medium using environment-friendly CDs.

Graphical Abstract

     

An Analysis of Vibrations and Rotations in the First Hydrogen Sulfide Hexade: the 4ν2 H $$_{2}^{{32}}$$ S Band

Optics and Spectroscopy - The infrared spectrum of the H2S molecule is recorded using a Bruker IFS 125HR Fourier transform spectrometer and studied in the range of 4500–5000 cm–1, in...     

Dimerization in the commensurate network of 4-n-octyl-4’-cyanobiphenyl (8CB) molecules adsorbed on MoS $_\mathsf{2}$ single crystal

By combining X-ray diffraction under grazing incidence (GIXD) and scanning tunneling microscopy (STM) measurements, we have determined the structure of 4-n-octyl-4-cyanobiphenyl (8CB) molecules adsorbed on MoS₂, under the thick organic film. The commensurability of the adsorbed network and the unit cell structure have been determined, revealing a complex 2D structure. This structure is characterized by straight ribbons with two types of ribbons, alternatively stacked. In one type, molecules are equally spaced, as they are paired in the other type. Considering the energetics of adsorption with a model of single ribbon, we recover the two observed ribbon structures. The alternate stacking of the ribbons appears as a consequence of the connection between the commensurabilities in the two main crystallographic directions. Moreover, we have found a particularly high value for the molecule-substrate potential corrugations, indicating that the dipole moment of 8CB molecules could play a fundamental role in the molecule-substrate interactions.Received: 1 April 2004, Published online: 29 June 2004PACS: 61.10.-i X-ray diffraction and scattering - 68.35.Bs Structure of clean surfaces (reconstruction) - 61.30.-v Liquid crystals - 68.35.Md Surface thermodynamics, surface energies     

Point defect diagrams for pure and doped nickel oxide $$ {hbox{N}}{{hbox{i}}_{{1} - delta }}{hbox{O}} $$ in the temperature range of 1,173–1,673 K (II)

The point defect diagrams in nickel oxide Ni_{1 - d}O {hbox{N}}{{hbox{i}}_{{1} - delta }}{hbox{O}} , pure and doped with M³⁺ and M⁺ metal ions, taking into consideration all of the types of defects in the cation sublattice, are presented in this work. A new method was used for the calculations of the diagrams. This method is based on the derived relations between the standard Gibbs energies of the formation of nickel vacancies and the intrinsic ionic and electronic defects. It also uses the experimental values of the deviation from the stoichiometry. The calculations were performed using the results of studies obtained by many authors in the temperature range of 1,173–1,673 K.     

Growth and characterization of Catena-((μ4-dihydrogen oxalate)-bis(μ3-hydrogen oxalato)-(μ2-dihydrogen oxalate)-tetra-aqua-di-rubidium) {Rb(HC2O4)(H2C2O4)(H2O)2}1∞ single crystal for nonlinear optical applications

A versatile, optically active, metal organic frame work, Catena-((μ₄-dihydrogen oxalate)-bis(μ₃-hydrogen oxalato)-(μ₂-dihydrogen oxalate)-tetra-aqua-di-rubidium) {Rb(HC₂O₄)(H₂C₂O₄)(H₂O)₂}¹∞ (CDBDTR), was grown by the process of slow evaporation using water as the solvent. Single XRD showed that the crystal belongs to the triclinic crystal system with the space group P1. The assigned vibrational frequencies of the compound were identified by the FTIR and FT-Raman techniques. The UV–Vis spectrum revealed the cut off wavelength of the crystal to be 233 nm, and due to this low cut off, it occupies a place in optoelectronic devices. Using the UV-spectra, several optical constants were assessed. The surface morphology was studied using HR-SEM analysis. Energy dispersive X-ray analysis (EDXA) confirmed the presence of rubidium in the crystal. The thermal stability of the crystal was investigated using TG/DTA analysis. The dielectric response of the grown crystal has been thoroughly analysed. A photoluminescence study showed that the crystal has a high degree of luminescence, and its single peak emission affirms its highly ordered crystalline nature. The life time was also analysed. The crystal offers adequate resistance to laser radiation with a threshold value of 4.78 GW/cm². By the Kurtz–Perry technique, the second harmonic generation of the crystal was assessed. The third order nonlinearity was explored using the Z-Scan technique. The figures of merit W and T were calculated in order to find the aptness of the crystal as a promising candidate for optical switching and optical limiting applications.     

Spectrophotometric determination of copper(II) in pharmaceutical,biological and water samples by 4-(2′-benzothiazolylazo)-salicylic acid

A highly sensitive method is proposed to determine copper(II) ions by forming a stable complex through their interaction with 4-(2′-benzothiazolylazo)-salicylic acid (BTAS) at room temperature and pH of about 5.0. The complex gave a maximum absorption at λ = 485 nm with a molar absorptivity coefficient of 2.35·10⁴ l/(mol·cm). The linear range for the copper determination is 0.63–5.04 mg/l. The method can be applied to determine copper ions in different biological specimens like some drugs and water samples.     

Quenching of tribo- and photoluminescence in a Tb2(SO4)3 · 8H2O + NaNO2 crystalline mixture

It is found that the addition of NaNO₂ to Tb₂(SO₄)₃ · 8H₂O crystals quenches tribo- and photo-luminescence from the latter. In the case of triboluminescence, the glow of both Tb³⁺* ions (solid component of triboluminescence) and N ₂ ^* molecules (gas component) is quenched. The NO ₂ ^? ion is known to be an efficient quencher of Tb³⁺ ion luminescence by the mechanism of radiationless energy transfer in solutions. That quenching takes place when a crystalline quencher is in contact with a crystalline phosphor and also with a gaseous (molecular) phosphor seems to indicate that the excitation energy is transferred not only within individual crystals but also between contacting surfaces of the phosphor and quencher and at the gas-solid interface.     

Study of the critical current density and the thermodynamic critical field in deuterated κ-(BEDT-TTF)2Cu[N(CN)2]Br organic superconductor

ABSTRACT

We have studied the reversible and irreversible part of the hysteresis loops as a function of slow cooling rate through the order–disorder transformation near 80?K for the deuterated (κ-D₈-Br) κ-(BEDT-TTF)₂Cu[N(CN)₂]Br organic superconductor. We estimated the critical current density J_C and the thermodynamic critical field H_C from the magnetic hysteresis loops. Temperature dependence of the critical current density derived from the irreversible part using Bean’s model. The thermodynamic critical field H_C has been obtained from the reversible part of the hysteresis loops.     

Lattice Dynamics of Bi2Те3 and Vibrational Modes in Raman Scattering of Topological Insulators MnBi2Te4·n(Bi2Te3)

JETP Letters - This work is devoted to the experimental study and symmetry analysis of the Raman-active vibration modes in MnBi2Te4·n(Bi2Te3) van der Waals topological insulators, where n is...     

Effect of hydrostatic pressure and temperature on the EPR spectrum of the Mn2+ ion in Zn(BF4)2 · 6H2O

A study of the effect of hydrostatic pressure and temperature on the EPR spectrum of the Mn²⁺ ion in Zn(BF₄)₂ · 6H₂O is reported. The break in the temperature dependence of the b ₂ ⁰ parameter at 196 K is evidence of the existence of a phase transition accompanied by a change in the thermal expansion coefficient. It is shown that pressure considerably affects the spectral parameters by reducing the axial parameter b ₂ ⁰ and increasing the cubic one, b ₄ ⁰ . At 9 kbar, the b ₂ ⁰ parameter is temperature independent. A comparison of the pressure dependences of the spectra of Zn(BF₄)₂ · 6H₂O, ZnSiF₆ · 6H₂O, ZnTiF₆ · 6H₂O, and MgSiF₂ · 6H₂O crystals suggests equal hydrogen-bond lengths in these compounds. A ligand hyperfine structure has been detected, which originates from the Zeeman interaction with the proton nuclei surrounding Mn²⁺ and manifests itself in the formation of satellites at each EPR line, their separation being proportional to the magnetic field. The nonlinear pressure dependence of the linewidth is related to the structural features of the crystal under study.     

Reexamination of the InSb(111) and GaSb(111) structures: Comment on ‘disorder in the reconstructed (111)2×2 surfaces of InSb and GaSb’ BY A. Belzner,E. Ritter and H. Schulz

A recent article [Surface Sci. 209 (1989) 379] has attempted to improve the agreement between our original X-ray diffraction data [Phys. Rev. Letters 54 (1985) 1275; Surface Sci. 186 (1987) 499] and the proposed distorted vacancy model by the introduction of an additional, partially occupied atom in the unit cell. Here we show that almost as much improvement can be obtained by introducing second-layer displacements into the original structure. This raises questions of uniqueness in crystallographic structure determination and the level of detail attainable without overinterpretation of data.     

Magnetic anisotropy and low-frequency dielectric response of weak ferromagnetic phase in κ-(BEDT-TTF)2Cu[N(CN)2]Cl, where BEDT-TTF is Bis(ethylenedithio)tetrathiafulvalene

We report a detailed characterization of the magnetism and AC transport in single crystals of the organic conductor -(BEDT-TTF)₂Cu[N(CN)₂]Cl by means of magnetic anisotropy measurements and low-frequency dielectric spectroscopy. Magnetic anisotropy obeys Curie-Weiss law with negative Curie-Weiss temperature in the temperature range 300 K-70 K. An antiferromagnetic transition with concomitant canted antiferromagnetic state is established at 22 K. A large hysteresis in the spin-flop transition and magnetic field reversal of the weak ferromagnetic magnetization are documented for the first time. A broad dielectric relaxation mode of moderate strength () emerges at 32 K, and weakens with temperature. The mean relaxation time, much larger than that expected for single-particle excitations, is thermally activated in a manner similar to the DC conductivity and saturates below 22 K. These features suggest the origin of the broad relaxation as an intrinsic property of the weak ferromagnetic ground state. We propose a charged domain wall in a random ferromagnetic domain structure as the relaxation entity. We argue that the observed features might be well described if Dzyaloshinsky-Moriya interaction is taken into account. A Debye relaxation with similar temperature dependence was also observed and seems to be related to an additional ferromagnetic-like, most probably, field-induced phase. We tentatively associate this phase, whose tiny contribution was sample dependent, with a Cu²⁺ magnetic subsystem. Received 15 June 1998 and Received in final form 1 February 1999     

IR and 1H NMR spectra of the strongly hydrogen-bonded complex (CF3COOH⋯OOCCF3)N(Bu)4 in organic solvents

The IR and ¹H NMR spectra are reported for tetra-n-butyl-ammonium di-trifluoroacetate in five dry aprotic solvents of different polarity (ε = 2.27–64.4). IR spectra correspond to pseudo-A type. The skeletal absorption and the continuous protonic absorption was separated numerically and for the later the integrated intensity, the centre of gravity and the mean frequency were derived and ΔH° value was estimated. The chemical shifts of H-bonded protons depend on the solvent ( δ = 18.76 ÷ 20.0 ppm) and is discussed with respect to specific interaction between the H-bonded complex and solvent.     

Inversion of spin levels in Ni2+: Zn(BF4)2 · 6H2O under uniform compression and the effect of transition coincidence

The electron paramagnetic resonance (EPR) spectra of Ni²⁺ ions substituting for Zn²⁺ ions in Zn(BF₄)₂ · 6H₂O crystals are studied over a wide range of temperatures under uniform compression. Measurements are performed in the X-and Q-bands. The parameter D, which characterizes the initial splitting, undergoes considerable variations with changes in temperature and pressure, whereas the g factor remains virtually unchanged. An increase in the temperature is accompanied by a nonlinear increase in D. Under uniform compression, the initial splitting varies linearly and the parameter D changes its sign at 3.5 kbar, which indicates inversion of the spin levels. The coincidence of the EPR lines associated with different transitions leads to the appearance of line-profile dips in the spectra due to cross-relaxation inside the spin system.