Random matrix theory for transition strength densities in finite quantum systems: Results from embedded unitary ensembles

Embedded random matrix ensembles are generic models for describing statistical properties of finite isolated interacting quantum many-particle systems. For the simplest spinless fermion (or boson) systems, with say m$m$ fermions (or bosons) in N$N$ single particle states and interacting via k$k$-body interactions, we have EGUE(k$k$) [embedded GUE of k$k$-body interactions] with GUE embedding and the embedding algebra is U(N)$U\left(N\right)$. A finite quantum system, induced by a transition operator, makes transitions from its states to the states of the same system or to those of another system. Examples are electromagnetic transitions (then the initial and final systems are same), nuclear beta and double beta decay (then the initial and final systems are different), particle addition to or removal from a given system and so on. Towards developing a complete statistical theory for transition strength densities (transition strengths multiplied by the density of states at the initial and final energies), we have derived formulas for the lower order bivariate moments of the strength densities generated by a variety of transition operators. Firstly, for a spinless fermion system, using EGUE(k$k$) representation for a Hamiltonian that is k$k$-body and an independent EGUE(t$t$) representation for a transition operator that is t$t$-body and employing the embedding U(N)$U\left(N\right)$ algebra, finite-N$N$ formulas for moments up to order four are derived, for the first time, for the transition strength densities. Secondly, formulas for the moments up to order four are also derived for systems with two types of spinless fermions and a transition operator similar to beta decay and neutrinoless beta decay operators. In addition, moments formulas are also derived for a transition operator that removes k₀$k_0$ number of particles from a system of m$m$ spinless fermions. In the dilute limit, these formulas are shown to reduce to those for the EGOE version derived using the asymptotic limit theory of Mon and French (1975). Numerical results obtained using the exact formulas for two-body (k=2$k=2$) Hamiltonians (in some examples for k=3$k=3$ and 4$4$) and the asymptotic formulas clearly establish that in general the smoothed (with respect to energy) form of the bivariate transition strength densities take bivariate Gaussian form for isolated finite quantum systems. Extensions of these results to bosonic systems and EGUE ensembles with further symmetries are discussed.     

Super-symmetric informationally complete measurements

Symmetric informationally complete measurements (SICs in short) are highly symmetric structures in the Hilbert space. They possess many nice properties which render them an ideal candidate for fiducial measurements. The symmetry of SICs is intimately connected with the geometry of the quantum state space and also has profound implications for foundational studies. Here we explore those SICs that are most symmetric according to a natural criterion and show that all of them are covariant with respect to the Heisenberg–Weyl groups, which are characterized by the discrete analog of the canonical commutation relation. Moreover, their symmetry groups are subgroups of the Clifford groups. In particular, we prove that the SIC in dimension 2, the Hesse SIC in dimension 3, and the set of Hoggar lines in dimension 8 are the only three SICs up to unitary equivalence whose symmetry groups act transitively on pairs of SIC projectors. Our work not only provides valuable insight about SICs, Heisenberg–Weyl groups, and Clifford groups, but also offers a new approach and perspective for studying many other discrete symmetric structures behind finite state quantum mechanics, such as mutually unbiased bases and discrete Wigner functions.     

Fabrication and Optimization of Poly(vinyl alcohol)/Zirconium Acetate Electrospun Nanofibers Using Taguchi Experimental Design

This paper presents an investigation regarding poly(vinyl alcohol)/zirconium acetate (organic–inorganic) (PVA/Zrace) nanofibers prepared by electrospinning which could be used as a precursor for fabricating ceramic metal oxide nanofibers. The effect of some processing variables, including polymer solution concentration, tip to collector distance and applied voltage of electrospinning, and the amount of Zrace and their interactions, on the diameter of the nanofibers were studied. Taguchi experimental design and a statistical analysis (ANOVA) were employed and the relationship between experimental conditions and yield levels determined. It was concluded that to obtain a narrow diameter distribution as well as maximum fiber fineness, a polymer concentration of 10 wt%, tip to collector distance of 18 cm and applied voltage of 20 kV variables were the optimum. Furthermore, it was also concluded that the ratio of Zrace (6 g) to PVA solution (10% wt) played an important role for achieving the minimum fiber diameter. Under these optimum conditions, the diameters of the electrospun composite fibers ranged from 86 nm to 381 nm with a diameter average of 193 nm. The experiments were done with Qualitek-4 software with “smaller is better” as the quality characteristics. The optimized conditions showed an improvement in the fibers diameter distribution and the average fibers diameter showed good resemblance with the result predicted using the Taguchi method and the Qualitek-4 software. The ANOVA results showed that all factors had significant effects on the fibers diameter and distribution, but the effect of PVA concentration and zirconium acetate were more significant than the other factors.     

Polymer-Nanoparticle Composites Composed of Poly(3-hydroxybutyrate-co-3-hydroxyvalerate) and Coated Silver Nanoparticles

The effects of addition of synthesized organic-suspension silver nanoparticles on the crystallization and thermal stability of poly(3-hydroxybutyrate-co-3-hydroxyvalerate) (PHBV) were studied by transmission electron microscopy (TEM), differential scanning calorimetry (DSC), wide-angle X-ray diffraction (XRD), UV-Vis absorption spectroscopy, polarized optical microscopy (POM), and thermal gravimetric analysis (TGA). The TEM images showed the average primary size of the as-synthesized silver nanoparticles, coated with a monolayer of the surfactants consisting of oleic acid and an alkylamine, was about 5 nm with narrow distribution, and that they were uniformly dispersed in n-heptane. PHBV/silver nanocomposites were prepared by melt mixing in an internal mixer and then injection molded into rectangle-shaped specimens by a labscale injection molding device. The coated silver nanoparticles showed a homogenuous dispersion in the PHBV matrix when the content of coated silver nanoparticles was about 1%. Both the DSC and POM data showed the efficient heterogeneous nucleation by the coated silver nanoparticles for facilitating PHBV crystallization. The thermal stability of the PHBV/silver nanocomposites improved with the increase in the content of the coated silver nanoparticles.     

Structural,optical and photocatalytic properties of (Mg,Al)-codoped ZnO powders prepared by sol–gel method

Structural and optical properties of 1 at % Al-doped Zn_1−xMg_xO (x=0–8%) powders prepared by sol–gel method were systematically investigated by means of X-ray diffraction, scanning electron microscopy, ultraviolet–visible absorbance measurement, photoluminescence and Raman scattering spectra. All the powders retained the hexagonal wurtzite structure of ZnO. The band gap and near band emission energies determined from absorbance and photoluminescence spectra increased linearly with increasing Mg content, respectively, which implied that the Mg worked effectively on ZnO band gap engineering, irrespective of Al codoping. However, according to the PL and Raman scattering studies, for the sample of x=8%, the Al doping efficiency was decreased by higher Mg codoping. On the other hand, the effect of Mg codoping on photocatalytic degradation of methylene orange was explored experimentally. The substitution of Mg ions at Zn sites shifted the conduction band toward higher energies and then enhanced the photocatalytic activity, while the incorporation of interstitial Mg ions and decreased Al doping efficiency for higher Mg doping sample (x=8%) reduced the photocatalytic activity.     

Preparation and characterization of “green” hybrid clay-dye nanopigments

We obtained a low cost and abundant nanopigment material composed of Rhodamine B (Rh-B) organic dye compound and Unye bentonite (UB) clay from Turkey. The characterization of the nanopigment was investigated using scanning electron microscopy (SEM), particle size distribution, powder X-ray diffraction (PXRD), Fourier transformed infra-red spectroscopy (FT-IR) and thermal analysis techniques. According to the result of texture analyses, we showed that the particle size distribution (d: 0.5-mean distribution) of Rh-B/UB nanopigment material was around 100 nm diameter. It was also demonstrated that the samples had a particle size around nm diameter in SEM images. As seen in the PXRD and thermal analysis, there is a difference in basal spacing by 1.46° (2θ) and a higher mass loss by 7.80% in the temperature range 200–500 °C compared to the raw bentonite.     

Kinetic study of isothermal crystallization process of Gd2Ti2O7 precursor's powder prepared through the Pechini synthetic approach

Crystallization process of Gd₂Ti₂O₇ precursor's powder prepared by Pechini-type polymerized complex route has been studied under isothermal experimental conditions in an air atmosphere. It was found that the crystallization proceeds through two-parameter Šesták–Berggren (SB) autocatalytic model, in the operating temperature range of 550 °C≤T≤750 °C. Based on the behavior of SB parameters (M, N), it was found that in the lower operating temperature range, the crystallites with relatively low compactness exist, which probably disclosed low dimensionality of crystal growth from numerous nucleation sites, where the amorphous solid is produced. In the higher operating temperature region (above 750 °C), it was established that a morphological well-defined and high-dimensional particles of the formed pyrochlore phase can be expected. It was found that at T=850 °C, there is a change in the rate-determining reaction step, from autocatalytic into the contracting volume mechanism.     

Stress evaluation of Through-Silicon Vias using micro-infrared photoelasticity and finite element analysis

The Through-SiliconVias (TSV) is a key component of three dimensional electronic packaging. Obtaining its stresses is very important for evaluating its reliability. A micro-infrared photoelasticity system with a thermal loading function was built and applied to characterize the stresses of the TSV structure. Through testing it was found that the stress of each TSV is different even if their fabrication technology is exactly the same, that different TSVs obtain their stress free states at different elevated temperatures, and that their stress free states are maintained even when the temperature is further elevated. A finite element model was used to quantitatively determine the stresses of a TSV under different stress-free temperatures. Different virtual photoelasticity fringe patterns were then created based on the principle of photoelasticity and the simulated stresses. Comparing the virtual fringe patterns with the experimental pattern, an appropriate virtual photoelasticity fringe pattern and the corresponding stresses of TSV were determined