Numerical calculation of the fidelity for the Kondo and the Friedel-Anderson impurities

The fidelities of the Kondo and the Friedel-Anderson (FA) impurities are calculated numerically. The ground states of both systems are calculated with the FAIR (Friedel artificially inserted resonance) theory. The ground state in the interacting systems is compared with a nullstate in which the interaction is zero. The different multi-electron states are expressed in terms of Wilson states. The use of N Wilson states simulates the use of a large effective number N _eff of states. A plot of ln(F) versus N ∝ ln(N _eff ) reveals whether one has an Anderson orthogonality catastrophe at zero energy. The results are at first glance surprising. The ln(F) – ln(N _eff ) plot for the Kondo impurity diverges for large N _eff . On the other hand, the corresponding plot for the symmetric FA impurity saturates for large N _eff when the level spacing at the Fermi level is of the order of the singlet-triplet excitation energy. The behavior of the fidelity allows one to determine the phase shift of the electron states in this regime.     

Determination of effective atomic number and electron density of heavy metal oxide glasses

The effective atomic number (Z_eff) and effective electron density (N_eff) of eight heavy metal oxide (HMO) glasses have been determined using the Monte Carlo simulation code MCNP for the energy range of 10?keV–10?MeV. The interpolation method was employed to extract Z_eff and N_eff values from the simulation and that calculated with the help of XCOM program. Comparisons are also made with predictions from the Auto-Z_eff software in the same energy region. Wherever possible, the simulated values of Z_eff and N_eff are compared with experimental data. In general, a very good agreement was noticed. It was found that the Z_eff and N_eff vary with photon energy and do not have extended intermediate regions where Compton scattering is truly dominating; only dips slightly above ～1.5?MeV were recorded. Z_eff and N_eff are found to increase with PbO and Bi₂O₃ contents. It was found that the Z_eff value rather than the N_eff value is a better indicator for PbO and/or Bi₂O₃ contents.     

Measurement of photon interaction parameters of high-performance polymers and their composites

In the present study, commercially important high-performance polymers and their composites have been investigated with respect to photon interactions as means of mass attenuation coefficient (μ/ρ), mean free path (MFP), half-value layer (HVL), effective atomic number (Z_eff), effective electron density (N_eff), and energy absorption and exposure buildup factors (EABF and EBF) at different photon energies. For this purpose, sample plates were prepared by extrusion and injection techniques using polyethersulfone, polyetherimide, acrylonitrile butadiene styrene copolymer, polyamide 66, polyphthalamide, and polypropylene copolymers as high-performance polymers and glass and carbon fibers as reinforcement. The (μ/ρ)s of the materials were measured at 81 and 356?keV photon energies to determine MFP, HVL, Z_eff, and N_eff. The theoretical values of these parameters were calculated via ZXCOM, WinXCom and Monte Carlo N-Particle simulation code (MCNP), and a good agreement was obtained between WinXCom–MCNP and MCNP–Exp. Finally, EABFs and EBFs of the samples were calculated up to around 40 MFP in the energy region 0.015–15?MeV and significant variations were observed in the continuous energy and MFP regions.     

Investigation of radiological properties of some shielding materials on charged and uncharged radiation interaction for neutron generator

Radiation interaction parameters such as total stopping power, projected range (longitudinal and lateral) straggling, mass attenuation coefficient, effective atomic number (Z_eff) and electron density (N_eff) of some shielding materials were investigated for photon and heavy charged particle interactions. The ranges, stragglings and mass attenuation coefficients were calculated for the high-density polyethylene(HDPE), borated polyethylene (BPE), brick (common silica), concrete (regular), wood, water, stainless steel (304), aluminum (alloy 6061-O), lead and bismuth using SRIM Monte Carlo software and WinXCom program. In addition, effective atomic numbers (Z_eff) and electron densities (N_eff) of HDPE, BPE, brick (common silica), concrete (regular), wood, water, stainless steel (304) and aluminum (alloy 6061-O) were calculated in the energy region 10?keV–100?MeV using mass stopping powers and mass attenuation coefficients. Two different methods namely direct and interpolation procedures were used to calculate Z_eff for comparison and significant differences were determined between the methods. Variations of the ranges, longitudinal and lateral stragglings of water, concrete and stainless steel (304) were compared with each other in the continuous kinetic energy region and discussed with respect to their Z_effs. Moreover, energy absorption buildup factors (EABF) and exposure buildup factors (EBF) of the materials were determined for gamma rays as well and were compared with each other for different photon energies and different mfps in the photon energy region 0.015–15?MeV.     

Microscopic calculations of ferroelectric instability in perovskite crystals

First-principles calculations are performed relating to the stability of a series of perovskite crystals with respect to transition to the ferroelectric and the antiferroelectric state. The calculations employ the generalized Gordon-Kim method, in which the total charge density of an ionic crystal is represented as a superposition of the densities of the individual ions. In the spirit of the nonequilibrium thermodynamics of Leontovich the charge density of an individual ion is calculated in the presence of external auxiliary fields which deform this density. Multipole deformations up to quadrupole are taken into account. The actual magnitude of the deformation is found by minimizing the total energy of the crystal in the Thomas-Fermi-Dirac approximation. The calculated values of the ion shifts in the ferroelectric phase for BaTiO₃, and also the electron contribution to the dielectric constant ε _∞ and the dynamic Born effective charges Z ^eff are found to be in good agreement with the experimental data. The proposed method allows one to obtain an analytical expression for ε _∞, Z ^eff, and the dynamic vibration matrix. It is shown that these expressions formally coincide with the expressions arising in the phenomenological models of the polarized and deformed ion. Analysis of the expressions obtained confirms the validity of the classical theory of ferroelectrics of displacement type for perovskite crystals. Zh. éksp. Teor. Fiz. 114, 333–358 (July 1998)     

Effects of off-resonance irradiation, cross-relaxation, and chemical exchange on steady-state magnetization and effective spin-lattice relaxation times

In the presence of an off-resonance radiofrequency field, recovery of longitudinal magnetization to a steady state is not purely monoexponential. Under reasonable conditions with zero initial magnetization, recovery is nearly exponential and an effective relaxation rate constant R_1eff = 1/T_1eff can be obtained. Exact and approximate formulas for R_1eff and steady-state magnetization are derived from the Bloch equations for spins undergoing cross-relaxation and chemical exchange between two sites in the presence of an off-resonance radiofrequency field. The relaxation formulas require that the magnetization of one spin is constant, but not necessarily zero, while the other spin relaxes. Extension to three sites with one radiofrequency field is explained. The special cases of off-resonance effects alone and with cross-relaxation or chemical exchange, cross-relaxation alone, and chemical exchange alone are compared. The inaccuracy in saturation transfer measurements of exchange rate constants by published formulas is discussed for the creatine kinase reaction.     

Gamma or X-rays attenuation properties of some biochemical compounds

The probability of gamma or X-ray interactions with important 14 antioxidants have been discussed for total photon interactions in the wide energy range of 1?keV–100?GeV using the WinXCOM code. The variations of mass attenuation coefficient (μ_ρ), effective atomic number (Z_eff) and electron density (N_el) with photon energy were plotted for total photon interactions. It was found that the values of μ_ρ, Z_eff and N_el depend on the incoming photon energy and chemical compositions of antioxidant. The highest values of these parameters were found at a low-energy zone where the photoelectric effect is the dominant interaction process. When antioxidants were compared with each other, it was seen that Z_eff has the highest values for Oenin chloride and Delphinidin chloride which contain the Cl element. This investigation is thought to be useful for medical applications where radiation exposure is present.     

Dependence of the Compton to Rayleigh intensity ratio on the scatterer atomic number in the range of 4(Be) to 31(Ga)

Compton to Rayleigh scattering intensity ratios (I_C/I_R) have been measured using X-rays with energy 17.44 keV for single-component materials with atomic number Z from 4 (Be) to 31 (Ga) and binary compounds of stoichiometric composition. The measurements have been performed using two optical schemes: an energy-dispersive X-ray fluorescence scheme with a molybdenum secondary target and wavelength-dispersive X-ray fluorescence one. The processing of the spectra was carried out by fitting with Pearson VII functions. For single-component and binary standards, the experimental dependence of the scattering intensity ratio on the atomic number was found to be the same. This confirms the additivity of the contribution of different atoms to the scattering. The dependence has a complex shape but is well described by the theoretical relationship for I_C/I_R with correction on the difference between Compton and Rayleigh radiation absorption coefficients. Two ranges of atomic number values are defined, in which the effective atomic number Z_eff can be determined by the calibration method using this dependence: for Z from 4 to 7 with low error of ΔZ_eff =±0.15 and for Z_eff from 10 to 18 with low error of ΔZ_eff =±0.69. A change in the shape of the Compton peak and an overestimated value of the of the Compton and Rayleigh peak intensity ratio when passing from a single-component scatterer (Al or Si) to their oxides Al₂O₃ or SiO₂, respectively, have been revealed.     

Quasiparticle recombination and 2Δ-phonon-trapping in superconducting tunneling junctions

The experimental recombination lifetime τ_eff of quasiparticles in superconducting films in general exceeds the intrinsic recombination lifetime τ _R by phonon trapping. On the basis of geometric acoustic propagation and reabsorption of phonons emitted in quasiparticle recombination, τ_eff is calculated as a function of film thicknessd taking into account longitudinal and transverse phonon reabsorption, bulk loss processes and acoustical phonon transmission into the substrate. With increasing thicknessd three characteristic ranges are found: range 1 with film thicknessd small compared to the phonon reabsorption mean free path Λ _w range 2 withd larger than Λ _w and dominating boundary losses, and range 3, also withd larger than Λ _w but with dominating bulk losses. For very smalld the relation between τ_eff and τ _R , the intrinsic recombination lifetime, contains only the limiting angle of total reflection of phonons within the superconducting film. Therefore, τ _R can be directly obtained by τ _eff measurements and from the sound velocities of the film-substrate system. Range 2 is characterized by a linear dependence of τ _eff ond. In this range it is not possible to obtain τ _R from τ _eff measurements, however, τ _eff allows a determination of the phonon boundary transmission. Range 3 shows no thickness dependence of τ _eff ond in the limit of larged values. In this range a further method for obtaining τ _R from τ _eff values is suggested.     

Unique dielectric properties in polyaniline/poly(vinylidene fluoride) composites induced by temperature variation

To explore an effect of temperature on the dielectric properties in polyaniline/poly(vinylidene fluoride) (PANI/PVDF) composites, the dielectric properties of these composites with different volumetric fractions of PANI (?_PANI) were studied in a wide temperature range. An increase in the effective conductivity (σ_eff) and dielectric permittivity (?_eff) was observed with increasing temperature in all PANI/PVDF composites. Particularly, for the composite with ?_PANI = 0.01, less than the percolation threshold (?_C = 0.045), the increase in σ_eff and ?_eff was most significant. A tunneling effect could be responsible for the unique dielectric properties. The results provided us useful information related to the microstructure of composites, which was not reported previously. (© 2008 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

A comparative study of gamma-ray interaction and absorption in some building materials using Zeff-toolkit

The gamma-ray shielding behaviour of a material can be investigated by determining its various interaction and energy-absorption parameters (such as mass attenuation coefficients, mass energy absorption coefficients, and corresponding effective atomic numbers and electron densities). Literature review indicates that the effective atomic number (Z_eff) has been used as extensive parameters for evaluating the effects and defect in the chosen materials caused by ionising radiations (X-rays and gamma-rays). A computer program (Z_eff-toolkit) has been designed for obtaining the mean value of effective atomic number calculated by three different methods. A good agreement between the results obtained with Z_eff-toolkit, Auto_Z_eff software and experimentally measured values of Z_eff has been observed. Although the Z_eff-toolkit is capable of computing effective atomic numbers for both photon interaction (Z_eff,PI) and energy absorption (Z_eff,En) using three methods in each. No similar computer program is available in the literature which simultaneously computes these parameters simultaneously. The computed parameters have been compared and correlated in the wide energy range (0.001–20?MeV) for 10 commonly used building materials. The prominent variations in these parameters with gamma-ray photon energy have been observed due to the dominance of various absorption and scattering phenomena. The mean values of two effective atomic numbers (Z_eff,PI and Z_eff,En) are equivalent at energies below 0.002?MeV and above 0.3?MeV, indicating the dominance of gamma-ray absorption (photoelectric and pair production) over scattering (Compton) at these energies. Conversely in the energy range 0.002–0.3?MeV, the Compton scattering of gamma-rays dominates the absorption. From the 10 chosen samples of building materials, 2 soils showed better shielding behaviour than did other 8 materials.     

Phase Transformations in Nd–Fe–B-Based Alloys under High Pressure Torsion at Different Temperatures

In this work, we studied the behavior of the Nd–Dy–Fe–Co–Cu–B alloy for permanent magnets under high pressure torsion (HPT). In the initial state of the studied alloy, it mainly contained the crystalline phase τ₁ (Nd, Dy)₂(Fe, Co, Cu) ₁₄B. After HPT at room temperature (T_HPT = 30°C), a mixture of an amorphous phase with nanocrystalline inclusions of the τ₁ phase is observed in the alloy. In the equilibrium phase diagram, this state is equivalent to a mixture of the τ₁ phase with the melt at the temperature T_eff= ∼1100°C. The thus determined T_eff value is called the effective temperature. When the T_HPT temperature of the HPT treatment increases to 300 and 400°C, the amorphous phase disappears, and the Fe₂B and γ-Fe phases appear instead. In the equilibrium phase diagram, this state is equivalent to a mixture of phases τ₁+ Fe₂B + γ-Fe, which is observed in the temperature range from ∼950 to ∼1050°C. We explain this phenomenon by the fact that with an increase in the HPT temperature T_HPT, the rate of formation of defects during deformation remains constant, but the rate of their thermal relaxation (annihilation) increases. This is equivalent to decrease in the effective temperature T_eff in the equilibrium phase diagram. The previously predicted decrease in T_eff with an increase in T_HPT is observed for the first time.

     

Quantum double and differential calculi

We show that bicovariant bimodules as defined by Woronowicz are in one-to-one correspondence with the Drinfeld quantum double representations. We then prove that a differential calculus associated to a bicovariant bimodule of dimension n is connected to the existence of a particular (n+1)-dimensional representation of the double. An example of bicovariant differential calculus on the nonquasitriangular quantum group E _q (2) is developed. The construction is studied in terms of Hochschild cohomology and a correspondence between differential calculi and 1-cocycles is proved. Some differences of calculi on quantum and finite groups with respect to Lie groups are stressed.     

Eine neue Methode zur Messung von Korrelationszeiten mit Hilfe von NMR-Impulsverfahren

We demonstrate a new method for the determination of correlation times. This method is based on examining the temperature dependence of coherent pulse averaging effects. We derive formulas for the temperature dependence of the decay time T_2eff of the transverse magnetization in the so called WHH and MW cases. As application of this method we measured T_2eff for OH-protons on a decationated Y-zeolite.     

Boron neutralization and hydrogen diffusion in silicon subjected to low-energy hydrogen implantation

Using the hydrogen neutralization of the boron acceptor, the diffusion of hydrogen is investigated in the temperature range 20 °–160 °C. The hydrogenation is performed by low-energy implantation. We observe a fast initial hydrogen migration, followed by a long-time diffusion phase that is described by an effective diffusion coefficientD _eff=D _{0 eff} exp(–E _a/kT) withD _{0 eff}–cm²s^–1 andE _a=(0.83±0.05) eV. No deeper hydrogen migration is detected for implantation times longer than – 30 min. Our data are explained by the build-up of a large amount of molecular hydrogen beneath the surface, which strongly hinders the transfer of the implanted hydrogen to the bulk. The thermal reactivation kinetics of the neutralized boron show a rapid initial step followed by a longtime thermally activated second order phase, which is limited by the recombination of hydrogen into molecules.     

Analytical performance of Compton/Rayleigh signal ratio by total reflection X-ray fluorescence (TXRF): A potential methodological tool for sample differentiation

The high sensitivity Compton and Rayleigh X-ray scattering signals can be used to gain valuable information on the chemical composition of various matrices, by exploiting the ratio of those signals as a function of the effective atomic number (Z_eff). Neither total reflection X-ray fluorescence (TXRF) nor the effect of the experimental setup, including sample preparation, X-ray excitation source selection, and band deconvolution procedure, has been assessed in this kind of approach. Here, a Compton/Rayleigh ratio and Z_eff-based TXRF method was set up and tested as an analytical tool for milk samples differentiation. The method was developed using a 90° scattering angle and assessed using different X-ray excitation sources: a molybdenum tube (Mo Kα 17.5 KeV) and a tungsten tube (W Lα 8.5 KeV and W-Brems 35 KeV). The evaluation of independent Compton and Rayleigh signals was performed by non-Gaussian and Gaussian curve resolution methods, and both height and area-based calculations were evaluated. Different sample preparation conditions were assessed. By using 11 standard materials, a calibration curve for Compton/Rayleigh ratio versus Z_eff was established. The method was tested to determine the Z_eff of milk samples, which enabled its use as a parameter to differentiate them. Good precisions were obtained with the Mo excitation source and the area-based calculations, which allowed to differentiate undiluted milk samples by species, treatment, and fat content according to their Compton/Rayleigh ratio. This simple and rapid method has the potential to be used for the differentiation of various types of samples, including liquids, solids, and aerosols.     

Effective magnetic anisotropy of nanocrystalline Nd-Fe-Ti-N hard magnetic alloys

The intermetallic compound Nd-Fe-Ti-N has been successfully synthesized by a mechanical alloying process. The structure and magnetic properties of the sample have been studied using X-ray diffraction and magnetic measurements. It is found that alloy exhibits a nanocrystalline ThMn₁₂-type tetragonal structure with lattice parameters of a=0.8723 nm and c=0.4896 nm. The saturation magnetization M_S and effective magnetic anisotropy K_eff of the compound have been determined by investigating magnetization processes. The calculated results based on the law of approach to magnetic saturation have been successfully used to determine the constant K_eff. The difference between observed and calculated values in magnetization is lower than 3%. Of all terms in the law of approach to saturation, it is the 1/H ² term, which is attributed more to non-compensated anisotropy energy, that has the prevailing effect for the compound. The absorption of nitrogen is found to increase unit cell volume, M_S and K_eff. Received: 28 October 1996 / Revised: 14 March 1997 and 4 August 1997 / Accepted: 8 August 1997     

Hilbert Modules and Stochastic Dilation of a Quantum Dynamical Semigroup on a von Neumann Algebra

A general theory for constructing a weak Markov dilation of a uniformly continuous quantum dynamical semigroup T _t on a von Neumann algebra ? with respect to the Fock filtration is developed with the aid of a coordinate-free quantum stochastic calculus. Starting with the structure of the generator of T _t , existence of canonical structure maps (in the sense of Evans and Hudson) is deduced and a quantum stochastic dilation of T _t is obtained through solving a canonical flow equation for maps on the right Fock module ?⊗Γ(L ²(ℝ₊,k ₀)), where k ₀ is some Hilbert space arising from a representation of ?^′. This gives rise to a *-homomorphism j _t of ?. Moreover, it is shown that every such flow is implemented by a partial isometry-valued process. This leads to a natural construction of a weak Markov process (in the sense of [B-P]) with respect to Fock filtration. Received: 15 June 1998/ Accepted: 4 March 1999     

Effective thermal conduction in composite materials

The problem of determining the bounds and/or estimating the effective thermal conductivity (λ _eff) of a composite (multiphase) system given the volume fractions and the conductivities of the components has been investigated. A comparison between the measured data and the results predicted by theoretical models has been made for seven heterogeneous samples. The tested models include those of the effective medium theory (EMT), Hashin and Shtrikman (HS) bounds, and Wiener bounds. These models can be used to characterize macroscopic homogeneous and isotropic multiphase composite materials either by determining the bounds for the effective thermal conductivity and/or by estimating the overall conductivity of the random mixture. It turns out that the most suitable one of these models to estimate λ _eff is the EMT model. This model is a mathematical model based on the homogeneity condition which satisfies the existence of a statistically homogeneous medium that encloses inclusions of different phases. Numerical values of thermal conductivity for the samples that satisfy the homogeneity condition imposed by the effective medium theory are in best agreement with the experimentally measured ones.     

Differential calculus on quantum Euclidean spheres

We study covariant differential calculus on the quantum Euclidean spheres S _q ^N−1 which are quantum homogeneous spaces with coactions of the quantum groups O _q (N). First order differential calculi on the quantum Euclidean spheres satisfying a dimension constraint are found and classified: ForN≥6, there exist exactly two such calculi one of which is closely related to the classical differential calculus in the commutative case. Higher order differential forms and symmetry are discussed. Presented at the 9th Colloquium “Quantum Groups and Integrable Systems”, Prague, 22–24 June 2000.