Testing the Distance-Duality Relation from Hubble,Galaxy Clusters and Type Ia Supernovae Data with Model Independent Methods

In this paper, we perform cosmological-model-independent tests for the distance-duality (DD) relation η(z)=D _L(1+z)^?2/D _A by combining the angular diameter distance D _A(or comoving distances D _c ) with the luminosity distance D _L. The D _A are provided by two galaxy clusters samples compiled by De Filippis et al. (the elliptical β model), Bonamente et al. (the spherical β model), the D _c are obtained from Hubble parameter data and D _L are given from the Union2.1 supernovae (SNe) Ia compilation. We employ two methods, i.e., method A: binning the SNe Ia data within the range Δz=|z?z _SNe|<0.005, and method B: reconstructing the D _L(z) by smoothing the noise of Union2.1 data set over redshift with the Gaussian smoothing function, to obtain D _L associated with the redshits of the observed D _A or D _c. Four parameterizations for η(z), i.e., η(z)=1+η ₀ z, η(z)=1+η ₀ z/(1+z), η(z)=1+η ₀ z/(1+z)² and η(z)=1?η ₀ ln(1+z), are adopted for the DD relation. We find that DD relation is consistent with the present observational data, and the results we obtained are not sensitive to the method and parameterization.     

Analytical model of a Brownian motor with a fluctuating potential

We propose a model of a Brownian motor that performs a useful work against a load force F in an asymmetric periodic potential V(x) = V(x + 2L) that undergoes random shifts by a half period L with a frequency γ. An arbitrarily shaped potential profile is repeated with an energy shift ΔV in both half-periods L, while the periodicity of the function V(x) is ensured by its jumps at x = 0 and x = L. The boundary condition at x = 0 for the distribution function of a Brownian particle allows us to introduce a high and narrow potential barrier V₀ that blocks the reverse current and leads to high efficiency of the motor (the ratio of the useful work done against the load force F to the energy imparted to the particle through the potential shifts). Based on this model, we derived exact analytical expressions for the current J and the efficiency η. In the special case of piecewise-linear potentials, J and η were plotted against F and γ for various values of the parameters ΔV and V₀. We discuss the influence of the potential shape and fluctuation frequency on the main characteristics of the motor.     

Spin-spin interaction and the EPR spectrum of KDy(WO<Subscript>4</Subscript>)<Subscript>2</Subscript>

The EPR spectrum of a KDy(WO₄)₂ monoclinic crystal is investigated. It is found that the EPR spectrum of magnetically concentrated materials at a low frequency (9.2 GHz) undergoes a substantial transformation in addition to the well-known broadening of the EPR lines. At low Dy³⁺ concentrations (x<10^?2), the EPR spectrum of an isomorphic crystal, namely, KY_(1?x)Dy_x(WO₄)₂, is characterized by the parameters g_x=0, g_y=1.54, and g_z=14.6. For a magnetically concentrated crystal KDy(WO₄)₂, the g values are as follows: g_x=0, g_y=0.82, and g_z=2.52. It is demonstrated that the difference in the parameters is associated with the specific spin-spin interaction between Dy³⁺ ions, including the Dzyaloshinski interaction, which is not observed at high frequencies.     

Josephson effects in unconventional heavy fermion superconductors

We discuss the Josephson effect for pairing states which break crystal symmetries in addition to gauge symmetry. We consider theE _1g andE _2u models for the low-temperature phase ofUPt ₃, with order parameters Δ(E _1g )～p _z (p _x +ip _y ) and Δ(E _2u )～p _z (p _x +ip _y )². We report calculations of Josephson critical currents, taking into account the effects of depairing at the interface. For singlet-triplet junctions the critical current is non-zero only for spin-orbit, spin-flip tunneling, and is found to be much smaller than the Ambegaokar-Baratoff value even when the spin-orbit tunneling amplitude is comparable to the spin-independent amplitude.     

Influence of the dimension of a polycrystalline film and the optical anisotropy of crystallites on the effective dielectric constant of the film

The dimension D of a polycrystalline film and the optical anisotropy m = ε_z/ε_x of uniaxial crystallites with the principal components ε_x = ε_y and ε_z of the tensor of the dielectric constant have been shown to produce a strong influence on the effective dielectric constant ε_D^* and the effective refractive index n_D^* = (ε_D^*)^1/2 of the film in the optical transparency region, as well as on the boundaries of the intervals B_Dl ≤ ε_D^* ≤ B_Du. The intervals Δ₂(m) = B_2l–B_2u and Δ₃(m) = B_3l–B_3u are separated by a gap for m in the range 1 < m < 2, whereas the theoretical dependence ε₂^*(m) is separated by a gap from the interval Δ₃(m) for m in the range 1 < m < 4. This is confirmed by a comparison of the experimental (n_oP) and theoretical (n_D^*) ordinary refractive indices for uniaxial polycrystalline films of the conjugated polymer poly(p-phenylene vinylene) (PPV) with uniaxial crystallites and appropriate values of m. In the visible transparency region of the PPV films with a change in m(λ) in the range 2 < m(λ) < 3 due to the dependence of the components ε_x,z(λ) on the light wavelength λ, the refractive indices n_oP²(λ) = ε_oP(λ) are consistent with the theoretical values of ε₂^*(λ) and lie outside the interval Δ₃(m). For m(λ) > 3 near the electronic absorption band of the crystallites, the values of ε_oP(λ) lie in the region of the overlap of the intervals Δ₂(m) and Δ₃(m). The boundaries mc of the range 1 < m < m_c are determined, for which the interval Δ₂(m) is separated by a gap from the dependences ε₃^*(m) corresponding to the effective medium theory with spherical crystallites and hierarchical models of a polycrystal, as well as from the proposed new dependence ε₃^*(m).     

Emergent nesting of the Fermi surface from local-moment description of iron-pnictide high-T<Subscript>c</Subscript> superconductors

We uncover the low-energy spectrum of a t-J model for electrons on a square lattice of spin-1 iron atoms with 3d _xz and 3d _yz orbital character by applying Schwinger-boson-slave-fermion mean-field theory and by exact diagonalization of one hole roaming over a 4 × 4 × 2 lattice. Hopping matrix elements are set to produce hole bands centered at zero two-dimensional (2D) momentum in the free-electron limit. Holes can propagate coherently in the t-J model below a threshold Hund coupling when long-range antiferromagnetic order across the d + = 3d _{(x + iy)z} and d ? = 3d _{(x ? iy)z} orbitals is established by magnetic frustration that is off-diagonal in the orbital indices. This leads to two hole-pocket Fermi surfaces centered at zero 2D momentum. Proximity to a commensurate spin-density wave (cSDW) that exists above the threshold Hund coupling results in emergent Fermi surface pockets about cSDW momenta at a quantum critical point (QCP). This motivates the introduction of a new Gutzwiller wavefunction for a cSDW metal state. Study of the spin-fluctuation spectrum at cSDW momenta indicates that the dispersion of the nested band of one-particle states that emerges is electron-type. Increasing Hund coupling past the QCP can push the hole-pocket Fermi surfaces centered at zero 2D momentum below the Fermi energy level, in agreement with recent determinations of the electronic structure of mono-layer iron-selenide superconductors.     

Hyperfine structure of the <Emphasis Type="Italic">S</Emphasis> levels of the muonic helium ion

Corrections of the α⁵ and α⁶ orders to the energy spectrum of the hyperfine splitting of the 1S and 2S levels of the muonic helium ion are calculated with the inclusion of the electron vacuum polarization effects, nuclear-structure corrections, and recoil effects. The values ΔE ^hfs(1S) = ?1334.56 meV and ΔE ^hfs(2S) = ?166.62 meV obtained for hyperfine splitting values can be considered as reliable estimates for comparison with experimental data. The hyperfine structure interval Δ₁₂ = 8ΔE ^hfs(2S) ? ΔE ^hfs(1S) = 1.64 meV can be used to verify QED predictions.     

Fine and hyperfine structure of <Emphasis Type="Italic">P</Emphasis>-wave levels in muonic hydrogen

Corrections of order α ⁵ and α ⁶ are calculated for muonic hydrogen in the fine-structure interval ΔE ^fs = E(2P _3/2) − E(2P _1/2) and in the hyperfine structure of the 2P _1/2-and 2P _3/2-wave energy levels. The resulting values of ΔE ^fs = 8352.08 μeV, ΔẼ ^hfs(2P _1/2) = 7819.80 μeV, and ΔẼ ^hfs(2P _3/2) = 3248.03 μeV provide reliable guidelines in performing a comparison with relevant experimental data and in more precisely extracting the experimental value of the (2P–2S) Lamb shift in the muonic-hydrogen atom. Original Russian Text ? A.P. Martynenko, 2008, published in Yadernaya Fizika, 2008, Vol. 71, No. 1, pp. 126–136.     

Stabilizer of a function in the gage group

It is proved that, for the dimension d of the stabilizer of an analytic function z(x, y) in the gage pseudogroup G = {z(x, y) → c(z(a(x), b(y))}, there are precisely four possibilities: (1) d = ∞ and the complexity of z is zero, (2) d = 3 and the complexity of z is equal to one, (3) d = 1 and z is equivalent the function r(x + y) ? x of complexity two, (4) d = 0 in all remaining cases.     

Ion-pair states of I<Subscript>2</Subscript>, Br<Subscript>2</Subscript>, IBr,and ICl

The experimentally determined energies and rotational constants of the vibrational levels v = 0–20 of the Ion-Pair states Ω = 0⁺, Ω = 1 of the I₂, Br₂, IBr, and ICl molecules are modeled. The model used includes three diabatic states, which correlate to X⁺(3P, 1D) + Y^～(1S₀). These states are coupled by the spin-orbit interaction, which is assumed to be independent of the internuclear distance. For IBr and ICl, as well as for the ungerade states of I₂ and Br₂, satisfactory results are obtained. The model is less applicable to the gerade states of I₂ and Br₂, which is possibly results from the retainment of the asymptotic J _A J _B coupling of the angular momenta at equilibrium internuclear distances.     

A new procedure for investigating three-dimensional stress fields in a thin plate with a through-the-thickness crack

In the paper, a new procedure is proposed to investigate three-dimensional fracture problems of a thin elastic plate with a long through-the-thickness crack under remote uniform tensile loading. The new procedure includes a new analytical method and high accurate finite element simulations. In the part of theoretical analysis, three-dimensional Maxwell stress functions are employed in order to derive three-dimensional crack tip fields. Based on the theoretical analysis, an equation which can describe the relationship among the three-dimensional J-integral J(z), the stress intensity factor K(z) and the tri-axial stress constraint level T _z (z) is derived first. In the part of finite element simulations, a fine mesh including 153360 elements is constructed to compute the stress field near the crack front, J(z) and T _z (z). Numerical results show that in the plane very close to the free surface, the K field solution is still valid for in-plane stresses. Comparison with the numerical results shows that the analytical results are valid.     

Spectral representation for singlet and triplet green's functions

Spectral representations of special Green functions are given explicitly. We consider the density correlation functionG ₂(x ₁ η ₁ x ₂ η ₂,x ₁ ⁺ η ₁ x ₂ ⁺ η′₂) and the functionG ₂(x ₁ η ₁ x ₁ ^? η₂,x ₂ η ₁ ^′ x ₂ ^? η ₂ ^′ Coupling the field operators Ψ^? (x, η), Ψ(x, η) to singlet and triplet operatorsA _{SMs TT3} (x), we obtain spectral representations for theseG-functions. The formulae derived may be of use when studying the system of equations for the Green functions, which describe many particle systems from a microscopic point of view.     

Ferroelectric phase transitions in ionic conductors based on bismuth vadanate

Ceramic solid solutions (Bi_{1 ? x} La _x )₄V₂O_{11 ? z} (I), Bi₄(V_{1 ? x} Fe _x )₂O_{11 ? y} (II), and (Bi_{1 ? x} La _x )₄(V_0.96Fe_0.04)₂O_{11 ? y} (III) (x = 0–0.3, step Δx = 0.02) are prepared using solid-phase synthesis. The concentration and temperature ranges of stabilization of different polymorphic modifications, including the ranges of concentrations x corresponding to the stabilization of the ferroelectric phase, are established. It is revealed that an increase in the concentration x in the region of existence of the pseudoorthorhombic phase α of the solid solutions studied leads to a decrease in the transition temperature, smearing of the transition, and an increase in the width of the thermal hysteresis of the ferroelectric phase transition. The effect of compressing of the domain walls by oxygen vacancies was revealed in the samples from the region of existence of the ferroelectric α phase, and the effect of dielectric relaxation was detected in the samples from the region of existence of the orthorhombic phase β.     

Colossal room-temperature magnetoresistance in thin La<Subscript>1−<Emphasis Type="Italic">x</Emphasis></Subscript>Ag<Subscript>y</Subscript>MnO<Subscript>3</Subscript> epitaxial films

The first thin La_1?xAg_yMnO₃ epitaxial films (_y ≤ x) were grown on SrTiO₃ (110) substrates with silver present in the ionized state (Ag⁺) only. The Curie temperatures T_C of the compositions with x = y = 0.05, x = y = 0.1, and x = 0.3 and y = 0.27 crystallizing in the hexagonal structure \(R\bar 3c\) above or close to room temperature. The temperature dependences of electrical resistivity ρ and of magnetoresistance ¦Δρ/ρ/¦ = ¦(ρ_H ? ρ _H = 0)/ρ_H=0¦ pass through maxima near T_C, with the magnetoresistance being negative and reaching colossal values of ～7–20% in a magnetic field H = 8.2 kOe not only at T_C but also at room temperature. The magnetic moment per formula unit as derived from the saturation magnetization at T = 5 K is substantially smaller than expected for complete ferromagnetic ordering. The magnetization in fields of up to 6 kOe depends on the actual sample cooling conditions, and the hysteresis loop of a field-cooled sample is displaced along the H axis by ΔH. The above properties can be accounted for by the fact that the films are in a two-phase magnetic (ferromagnetic-antiferromagnetic) state induced by strong s-d exchange. The maximum value of Δ H was used to calculate the energy of exchange coupling between the ferromagnetic and antiferromagnetic parts of a sample.     

Symbiotic organism search algorithm for simulation of <Emphasis Type="Italic">J</Emphasis>-<Emphasis Type="Italic">V</Emphasis> characteristics and optimizing internal parameters of DSSC developed using electrospun TiO<Subscript>2</Subscript> nanofibers

In the present investigation, the recently developed, simple, robust, and powerful metaheuristic symbiotic organism search (SOS) algorithm was used for simulation of J-V characteristics and optimizing the internal parameters of the dye-sensitized solar cells (DSSCs) fabricated using electrospun 1-D mesoporous TiO₂ nanofibers as photoanode. The efficiency (η =?5.80%) of the DSSC made up of TiO₂ nanofibers as photoanode is found to be ～ 21.59% higher compared to the efficiency (η =?4.77%) of the DSSC made up of TiO₂ nanoparticles as photoanode. The observed high efficiency can be attributed to high dye loading as well as high electron transport in the mesoporous 1-D TiO₂ nanofibers. Further, the validity and advantage of SOS algorithm are verified by simulating J-V characteristics of DSSC with Lambert-W function.     

Quark-antiquark composite systems: The Bethe-Salpeter equation in the spectral-integration technique

The Bethe-Salpeter equations for the quark-antiquark composite systems, q\(\bar q\), are written in terms of spectral integrals. For the q\(\bar q\) mesons characterized by the mass M, spin J, and radial quantum number n, the equations are presented for the following (n, M²) trajectories: π _J , η _J , a _J , f _J , ρ _J , ω _J , h _J , and b _J .     

Raman scattering spectroscopy of inclusions of carbon in Al<Subscript>2</Subscript>O<Subscript>3</Subscript> films and its solid solutions with HfO<Subscript>2</Subscript>

We apply Raman scattering spectroscopy to study the nature of carbon inclusions in Al₂O₃ and (HfO₂) _x (Al₂O₃)_{1 ? x} films deposited using volatile complex compounds. Raman spectra of the films under investigation contain D and G vibrational modes, which indicate that carbon clusters of the sp ² configuration tend to form in the films. We estimate the size of clusters from the integrated intensity ratio I _D /I _G and find it to be in the range of 14–20 Å. The content of hydrogen in carbon clusters is calculated from the height of the photoluminescence pedestal and is found to vary from 14 to 30 at % depending on the regime of the film’s synthesis.     

Spectroscopy of optical centers of Eu<Superscript>3+</Superscript> ions in partially stabilized and stabilized zirconium crystals

The structure of the optical centers of Eu³⁺ ions in tetragonal (ZrO₂)_1–x–y (Y₂O₃) _x (Eu₂O₃) _y (х = 2.7–3.6; y = 0.1) and cubic (ZrO₂)_1–x–y (Y₂O₃) _x (Eu₂O₃) _y (х = 8–38; y = 0.1–0.5) crystals of solid solutions on the basis of zirconium dioxide is studied using the methods of optical and Raman-scattering spectroscopy. Characteristic optical centers of Eu³⁺ ions with different crystalline environments are revealed in the above compounds.     

Long-range spin correlations in a honeycomb spin model with a magnetic field

We consider the spin-1/2 model on the honeycomb lattice [A. Kitaev, Ann. Phys. 321, 2 (2006)] in the presence of a weak magnetic field h _α ? J. Such a perturbation treated in the lowest nonvanishing order over h _α leads [K.S. Tikhonov, M.V. Feigel’man, and A.Yu. Kitaev, Phys. Rev. Lett. 106, 067203 (2011)] to a powerlaw decay of irreducible spin correlations 《s ^z (t, r)s ^z (0, 0)》 ∝ h _z ² f(t, r), where f(t, r) ∝ [max(t, Jr)]^–4. We have studied the effects of the next order of perturbation in h _z and found an additional term of the order h _z ⁴ in the correlation function 《s ^z (t, r)s ^z (0, 0)》 which scales as h _z ⁴ cosγ/r ³ at Jt? r, where γ is the polar angle in the 2D plane. We demonstrate that such a contribution can be understood as a result of a perturbation of the effective Majorana Hamiltonian by the weak imaginary vector potential A _x ∝ i h _z ² .