Entropy squeezing and entanglement of the interaction between SU(1,1) and SU(2) quantum systems

The problem of the interaction between two quantum systems namely SU(1,1) and SU(2) is considered. Using the evolution operator technique, an exact solution of the wave function and consequently the density matrix are obtained. The entropy squeezing is examined and it has shown that, different values of the relative phase angle ? as well as the coupling parameter λ lead to different observation of the squeezing in the quadratures. In the meantime, we have shown that the entropy squeezing is also sensitive to the variation in the state angle θ, the detuning parameter Δ in addition to the excitation number m. Moreover, for a large value of the detuning parameter there is a weak entanglement between the atom and the quantum system and vice versa. Furthermore, we find that the Q-function is sensitive to the variation in the excitation number m in addition to the Bargmann index k where the nonclassical effect is pronounced for the even parity.     

Electrochemical and structural properties of a polymer electrolyte system based on the effect of CeO<Subscript>2</Subscript> nanofiller with PVDF-co-HFP for energy storage devices

In the present work, a series of five different nanocomposite polymer electrolytes (NCPEs) have been reported with varying contents of ceria, CeO₂ nanofiller suitably incorporated within an optimized composition having 75:25 wt% ratio of poly(vinylidenefluoride-co-hexafluoropropylene) [(PVDF-co-HFP)] and zinc trifluoromethanesulfonate (ZnTf) in the form of films obtained by mean of solution casting technique with a general formula [75 wt% PVDF-co-HFP:25 wt% ZnTf]-x wt% CeO₂ where x = 1, 3, 5, 7, and 10, respectively. The chosen NCPE system is found to exhibit the maximum electrical conductivity of 3 × 10^?4 S cm^?1 for 5 wt% loading of CeO₂ nanofiller at ambient temperature. The observed conductivity enhancement has been attributed to the occurrence of an increase in the amorphous content as confirmed by X-ray diffraction (XRD) analysis. Detailed Fourier transform infrared (FTIR) spectral analysis has indicated the feasibility of complexation of the host polymer matrix with ZnTf salt and CeO₂ nanofiller. The incorporation of CeO₂ nanofiller has further increased the decomposition voltage of the polymer electrolyte from 2.4 to 2.7 V as revealed from the voltammetric studies performed on such NCPEs, thereby suggesting the suitability of these NCPE films with an enhanced electrical conductivity as new electrolytes in order to design and fabricate eco-friendly zinc rechargeable batteries and other electrochemical devices.     

Exciton effects on the refractive index and optical absorption in wurtzite quantum wells via a fractional-dimensional space approach

The optical refractive index changes and absorption coefficients of quantum wells (QWs) are theoretically investigated with considering exciton effects within the framework of the fractional-dimensional space approach. The exciton wave functions and bound energies are obtained as a function of spatial dimensionality, and the dimension increases with the well width increasing. Then optical properties are obtained by using the compact-density matrix approach and an iterative method. Numerical results are presented for wurtzite ZnO/Mg_xZn_1−xO QWs. The calculated results show that the changes of refractive index and absorption coefficients are greatly enhanced due to the quantum confinement of exciton. And the smaller the QW width (dimension) is, the larger influence of exciton on the optical properties will be. Furthermore, the exciton effects make the resonant peaks move to a lower energy. In addition, the optical properties are related to the QW width, the incident optical intensity and carrier density.     

On exact master equation for an open system

An exact equation is obtained for the evolution of density matrix in the coherent state representation for the open system of a single harmonic oscillator coupled to a reservoir of N oscillators.     

Evaluation of the geopolymer/nanofiber interfacial bond strength and their effects on Mode-I fracture toughness of geopolymer matrix at high temperature

The present article has reported the effects of several nanofiller’s aspect ratio, length and interfacial strength on Mode-I fracture toughness (K_IC) of geopolymer as the matrix of continuous fibre reinforced composites. These nanofillers have been chosen based on the variations in the surface chemistry and nature of interfacial bonding with geopolymer, which include Carbon, Alumina and Silicon carbide. Geopolymer matrix was subjected to the addition of single volume fraction, 2% of each type of nanofiller with two aspect ratios, designated as nanoparticles and nanofibers. Notched beam flexure tests (SEVNB) of neat and each nanofiller reinforced samples suggest that, while baseline K_IC of neat geopolymer improved with heat treatment, nanofibers with high interfacial bond strength showed maximum capability in further improving K_IC. Among those nanofibers, 2 vol% Silicon Carbide Whisker (SCW) showed the largest improvement in K_IC of geopolymer, which is ~164%. After heat treatment at 650 °C, SCW reinforcement was also found to be effective, with only ~28% lower than the reinforcing performance at 250 °C, while the performance of Alumina Nanofiber reinforced geopolymer notably reduced. SEM and EDS analysis suggested that the inhomogeneity in neat geopolymer and length of nanofibers control the reinforcing capability as well as crack propagation resistance of geopolymer. For instance, minimum length of nanofillers to toughen this geopolymer at 250 °C was required as ~2 μm. The results further suggested that the sample failure occurred due to the dominance of tensile failure of nanofibers over the interfacial separation.     

Calculation of Double-Quantum-Coherence Two-dimensional Spectra: Distance Measurements and Orientational Correlations

The double-quantum-coherence (DQC) echo signal for two coupled nitroxides separated by distances ?10 Å, is calculated rigorously for the six-pulse sequence. Successive application of six pulses on the initial density matrix, with appropriate inter-pulse time evolution and coherence pathway selection leaves only the coherent pathways of interest. The amplitude of the echo signal following the last π pulse can be used to obtain a one-dimensional (1D) dipolar spectrum (Pake doublet), and the echo envelope can be used to construct the 2D DQC spectrum. The calculations are carried out using the product space spanned by the two electron-spin magnetic quantum numbers m ₁, m ₂ and the two nuclear-spin magnetic quantum numbers M ₁, M ₂, describing, e.g. two coupled nitroxides in bilabeled proteins. The density matrix is subjected to a cascade of unitary transformations taking into account dipolar and electron exchange interactions during each pulse and during the evolution in the absence of a pulse. The unitary transformations use the eigensystem of the effective spin Hamiltonians obtained by numerical matrix diagonalization. Simulations are carried out for a range of dipolar interactions, D, and microwave magnetic field strength B ₁ for both fixed and random orientations of the two ¹⁴N (and ¹⁵N) nitroxides. Relaxation effects were not included. Several examples of 1D and 2D Fourier transforms of the time-domain signals versus dipolar evolution and spin-echo envelope time variables are shown for illustration. Comparisons are made between 1D rigorous simulations and analytical approximations. The rigorous simulations presented here provide insights into DQC electron spin resonance spectroscopy, they serve as a standard to evaluate the results of approximate theories, and they can be employed to plan future DQC experiments.     

A model for the temperature dependence of the viscosity in Cu–As–Se system

The microscopic bonding behavior of amorphous Cu_x(As₂Se₃)_1?x (x = 0.00, 0.01, 0.05, 0.10 and 0.20) is studied from the point of view of the viscosity. The model used in this analysis describes the temperature dependence of the viscosity in terms of the mean bond strength E₀, the mean coordination number Z₀, and their fluctuations ΔE, ΔZ of the structural units that form the melt. The model reproduces quite well the temperature dependence of the viscosity of Cu_x(As₂Se₃)_1?x observed experimentally. According to the theory, the fragility of the system increases as the fluctuation of the total bond strength increases. It is shown that the viscous flow is accompanied by the cooperative movements of the structural units and occurs by breaking selectively the weaker parts of the bonds between the structural units. This notion is related to the concept of Cooperatively Rearranging Region (CRR) in the theory of Adam–Gibbs. By analyzing the model, the fluctuation of the total bond strength in Cu–As–Se system is evaluated quantitatively, and the composition dependence of the fragility is discussed in terms of bond strength and the coordination number between the structural units. The analysis suggests that in the Cu_x(As₂Se₃)_1?x system, there must be a strong composition dependence in the bond strength and a weak composition dependence in the fragility and coordination number fluctuation.     

Light scattering and absorption by densely packed groups of spherical particles

Light scattering by clusters of spheres is investigated using numerical light scattering simulations. We consider clusters with density of 0.1-30%. Simulations are carried out for various real part of refractive indices (i.e., 1.01, 1.10, 1.31, 1.60, and 2.00) and for two values of the imaginary part of the refractive index (0 and 0.01) of spheres in the cluster. All spheres in the cluster have the same size (kr=4, k=2π/λ, r is the radius of the sphere, λ is the wavelength of the incident light).The obtained results include behaviors of cross sections as functions of densities (up to 30%), investigation of the influence of multiple scattering inside the media on the cross sections, and influence of densities on phase matrix elements (PMEs) and parameters obtained from the PMEs such as the cross polarization ratio, degree of linear depolarization, entropy, etc.In addition, we also investigate the influence of particle size for the same total volume of the cluster on cross sections. The outer radius R of the cluster of spheres was constant and equal to 40/k in all calculations.     

Optical and electronic polarizability investigation of Nd-doped soda-lime silicate glasses

This paper reports on different physical and optical properties of Nd³⁺-doped soda-lime silicate glass. The glasses containing Nd³⁺ in (65−x)SiO₂:25Na₂O:10CaO:xNd₂O₃ (where x=0.0-5.0 mol%) have been prepared by the melt-quenching method. In order to understand the role of Nd₂O₃ in these glasses the density, molar volume, refractive index and optical absorption were investigated. The results show that the density and molar volume of the glasses increase with an increase in Nd₂O₃ concentration and consequently generate more non-bridging oxygen (NBOs) into glass matrix. The optical absorption spectra were measured in the wavelength range from 300 to 700 nm and the optical band gaps were determined. It was found that the optical band gap decreases with an increase in Nd₂O₃ concentration. On the basis of the measured values of density and refractive index, the Nd³⁺ ion concentration in glasses, the polarizability of oxide ions and optical basicity were theoretically determined.     

On the Distribution of the Wave Function for Systems in Thermal Equilibrium

For a quantum system, a density matrix ρ that is not pure can arise, via averaging, from a distribution μ of its wave function, a normalized vector belonging to its Hilbert space ?. While ρ itself does not determine a unique μ, additional facts, such as that the system has come to thermal equilibrium, might. It is thus not unreasonable to ask, which μ, if any, corresponds to a given thermodynamic ensemble? To answer this question we construct, for any given density matrix ρ, a natural measure on the unit sphere in ?, denoted GAP(ρ). We do this using a suitable projection of the Gaussian measure on ? with covariance ρ. We establish some nice properties of GAP(ρ) and show that this measure arises naturally when considering macroscopic systems. In particular, we argue that it is the most appropriate choice for systems in thermal equilibrium, described by the canonical ensemble density matrix ρ_β = (1/Z) exp (?β H). GAP(ρ) may also be relevant to quantum chaos and to the stochastic evolution of open quantum systems, where distributions on ? are often used.     

Determination of the final nucleus density matrix by measuring the angular correlation of charged particles and γ-quanta in various planes

The measurements of the angular correlation function of charged particles and γ-quanta emitted by a final even-even nucleus in state J_f in different planes of γ-quantum ejection with respect to the reaction plane have been shown to offer the unique possibility of restoring all the even-rank components of the model-less density matrix in the transitions with J_f = L (L) is the multipolarity of the γ-transition). The minimum number of planes in which the angular correlation function should be measured to restore the density matrix has been found. The formulas relating the components of the model-less density matrix to the polarization characteristics of an even-even nucleus in a given state have been obtained.     

Fluoride glasses in the InF3-GaF3-YF3-PbF2-CaF2-ZnF2 system

New glasses have been synthesized in a multicomponent system based on indium fluoride. Samples of a few mm in thickness were obtained. They are transparent and homogeneous. Main physical properties such as density, characteristic temperatures, density, thermal expansion and refractive index have been measured. The evolution versus composition is reported for samples with the formula: (35−x) InF₃-xGaF₃-10YF₃-25PbF₂-15CaF₂-15ZnF₂. T_g lies between 260 and 296 °C while melting starts around 480 °C. Glass samples are stable at room temperature. By comparison with other standard fluoride glasses, they exhibit higher refractive index and density.     

Computational approach to estimate layer structures of organic derivatives of boehmite

The observed basal spacings of the alkyl derivatives of boehmite, AlO(OH)_1−x(OR)_x, obtained by the reaction of aluminum metal or aluminum alkoxides with alcohols at 250–300 °C was only slightly affected by the population (x) of the alkyl groups (x=0.39−0.21) (Chem. Mater. 12 (2000) 55). In order to clarify the origin of this independency, the molecular mechanics (MM) calculation was carried out, and the effect of the alkyl population upon the basal spacing of the butyl derivative of boehmite, AlO(OH)_1−x(OCH₂CH₂ CH₂CH₃)_x, was examined in a range of x=0.00–0.30. The calculated results clearly suggested that in the range of x from 0.3 to 0.2, the boehmite derivative has the bilayer arrangement of the alkyl groups with essentially all-trans conformation. In this range, the basal spacing was only slightly affected by the population of the alkyl groups because it is determined by the most crowded part of the assembly of the alkyl chains. Since the alkyl chains are fixed to the host layers through the covalent bonding, decrease in the alkyl population does not affect essential feature of the alkyl derivatives of layered inorganics.     

Theoretical study of the optical absorption and refraction index change in a cylindrical quantum dot

Analytical expressions of the optical absorption coefficient and the change in refractive index associated with intraband relaxation in a cylindrical quantum dot are obtained by using the density matrix formalism. Energy levels in conduction band were calculated with finite confining potential in the framework of the effective-mass envelope-function theory. Numerical calculations on a typical GaAs/AlβGa1−βAs QD are performed. It is found that the absorption and refraction index change sensitively depend not only on the incident optical wave but also on the dot size and the Al mole fraction β in the AlβGa1−βAs material.     

Effects of the phase transition in Hg2(Br,I)2 crystals

The effects of the phase transition in Hg₂(Br,I)₂ crystals have been investigated over a wide range of temperatures by the Raman scattering spectroscopy and X-ray diffraction analysis. The overtones (at the X point of the Brillouin zone boundary) and the fundamental tones (at the center of Brillouin zone) of soft modes are found in the Raman spectra of these crystals and studied in detail. The density of one-phonon states of the soft TA branch manifests itself in the Raman spectra of mixed crystals. The potentialities of the soft-mode spectroscopy are realized in full measure. Analysis of the ratio between intensities of overtones and fundamental tones of the soft modes has demonstrated the applicability of the Landau phenomenological theory of phase transitions. The orthorhombic splitting of the reflections corresponding to the basal plane is revealed in the X-ray diffraction patterns and thoroughly explored. The temperature dependences of the isotropic and shear spontaneous strains are obtained. It is shown that the shear spontaneous strain plays a decisive role. The critical indices are determined and the model of the improper ferroelastic phase transition D _4h ¹⁷ → D _2h ¹⁷ in the vicinity of the tricritical point is corroborated.     

Evolution of a finite Olver beam propagating in a right handed and double negative index slab system

In this work, we investigate the evolution of a first order finite Olver beam and a zeroth order one (finite Airy beam) propagating in a right handed and double negative index cascaded slab system based on the transfer matrix and generalized Huygens-Fresnel integral equation. It is discovered that the incident finite Olver beam could reappear on the output cross section by using a periodic slab system with a negative index material as long as n_l=??n_r, L?=?R; for n_l≠?n_r, the bigger abs(n_l) is, the longer the needed unit length L to achieve an original beam intensity reproduction, and vice versa; the relations between the negative refractive index and the double negative material unit length are also quantitative explored by using the Origin Lab. It is expected that the derived analytical formulae and conclusions can provide a convenient and effective way for studying the evolution of a finite Olver beam propagating in multilayered structures, especially for periodic and quasi-periodic slab systems.     

Influence of interlayer coupling and intra-layer Coulomb interaction on electronic transport in bilayer graphene

Calculations of renormalized perpendicular conductivity within Kubo formula employing single particle temperature dependent Green's function formalism for bilayer graphene has been attempted. On the basis of numerical analysis, perpendicular conductivity as a function of temperature, interlayer coupling, onsite Coulomb interaction and carrier concentration per site has been analyzed for both AA- and AB-stacked bilayer graphene. It is found that perpendicular conductivity increases with interlayer coupling and also with temperature at low temperatures while at higher temperatures, there is saturation in perpendicular conductivity. Influences of onsite Coulomb interaction and carrier concentration per site on perpendicular conductivity is just opposite to each other while onsite Coulomb energy suppresses the rate of increase of σ_⊥/σ_⊥0 with temperature, on the other hand increase in carrier density per site enhance this rate significantly. Finally, theoretically obtained results on temperature dependent perpendicular conductivity are viewed in terms of electronic transport data as well as recent theoretical works available in bilayer graphene.     

A study of the generalized density matrix in the SU(3) model of Elliott for an arbitrary oscillator n-shell

The SU(3) model of Elliott for an arbitrary oscillator n-shell is considered. Exact solutions corresponding to the low-lying collective SU(3) multiplets are obtained. These multiplets exhibiting distinct collective properties are used as a “collective band”. All the matrix elements from the one-particle density matrix operator inside a given band are investigated. The so-formed matrix R, i.e. the generalized density matrix (GDM), is diagonalized and an explicit expression for the eigenvalues of the GDM in the case of low-lying multiplets is found. The GDM diagonal form contains a number of vanishing eigenvalues (the number of such “zero” eigenvalues is equal to that of the occupied orbits in the oscillator n-shell). Most of the remaining eigenvalues are close to unity. The asymptotic behaviour of the nonzero eigenvalues is analyzed in the limit of large nucleon number and the accuracy of the normalization condition R²= R is estimated.     

Spin and the Thermal Equilibrium Distribution of Wave Functions

Consider a quantum system S weakly interacting with a very large but finite system B called the heat bath, and suppose that the composite S∪B is in a pure state Ψ with participating energies between E and E+δ with small δ. Then, it is known that for most Ψ the reduced density matrix of S is (approximately) equal to the canonical density matrix. That is, the reduced density matrix is universal in the sense that it depends only on S’s Hamiltonian and the temperature but not on B’s Hamiltonian, on the interaction Hamiltonian, or on the details of Ψ. It has also been pointed out that S can also be attributed a random wave function ψ whose probability distribution is universal in the same sense. This distribution is known as the “Scrooge measure” or “Gaussian adjusted projected (GAP) measure”; we regard it as the thermal equilibrium distribution of wave functions. The relevant concept of the wave function of a subsystem is known as the “conditional wave function.” In this paper, we develop analogous considerations for particles with spin. One can either use some kind of conditional wave function or, more naturally, the “conditional density matrix,” which is in general different from the reduced density matrix. We ask what the thermal equilibrium distribution of the conditional density matrix is, and find the answer that for most Ψ the conditional density matrix is (approximately) deterministic, in fact (approximately) equal to the canonical density matrix.     

Magnetic resonance imaging for secondary assessment of breast density in a high-risk cohort

A quantitative measure of three-dimensional breast density derived from noncontrast magnetic resonance imaging (MRI) was investigated in 35 women at high-risk for breast cancer. A semiautomatic segmentation tool was used to quantify the total volume of the breast and to separate volumes of fibroglandular and adipose tissue in noncontrast MRI data. The MRI density measure was defined as the ratio of breast fibroglandular volume over total volume of the breast. The overall correlation between MRI and mammographic density measures was R²=.67. However the MRI/mammography density correlation was higher in patients with lower breast density (R²=.73) than in patients with higher breast density (R²=.26). Women with mammographic density higher than 25% exhibited very different magnetic resonance density measures spread over a broad range of values. These results suggest that MRI may provide a volumetric measure more representative of breast composition than mammography, particularly in groups of women with dense breasts. Magnetic resonance imaging density could potentially be quantified and used for a better assessment of breast cancer risk in these populations.