From 4d superconformal indices to 3d partition functions

An exact formula for partition functions in 3d field theories was recently suggested by Jafferis, and Hama, Hosomichi, and Lee. These functions are expressed in terms of specific q-hypergeometric integrals whose key building block is the double sine function (or the hyperbolic gamma function). Elliptic hypergeometric integrals, discovered by the second author, define 4d superconformal indices. Using their reduction to the hyperbolic level, we describe a general scheme of reducing 4d superconformal indices to 3d partition functions which imply an efficient way of getting 3dN=2 supersymmetric dualities for both SYM and CS theories from the “parent” 4dN=1 dualities for SYM theories. As an example, we consider explicitly the duality pattern for 3dN=2 SYM and CS theories with SP(2N) gauge group with the antisymmetric tensor matter.     

The parallelizing S7 torsion in gauged N=8 supergravity

Using the parallelizing S⁷ torsion as an ansatz we investigate two solutions of gauged N=8 supergravity with SO(7) invariance. Supersymmetry is uniformly broken. We calculate the masses for these solutions which are both unstable. Certain apparent discrepancies with the results obtained by spontaneous compactification of d=11 supergravity are discussed. We establish that the compactification on the parallelized S⁷ has an SO(7) invariance and clarify the issue of supersymmetry breaking. The lack of stability in d=4 indicates that this d=11 solution is unstable.     

Stark-Effekt-Untersuchungen in der Hyperfeinstruktur der 3s 2 3d 2 D 5/2- und2 D 3/2-Terme des Al I-Spektrums

The resonance fluorescence of the transitions 3d ² D _5/2,3/2 3p ² P _3/2,1/2 in the Al I-spectrum was observed as a function of a magnetic field. Adding an electric field parallel to the magnetic field the shifts of level crossing signals caused by the Stark effect of the electric field were used to separate overlapping signals of the 3d ² D _5/2- and 3d ² D _3/2-states. The following values of the Stark parametersβ of both states and the hyperfine structure constantsA andB of the 3d ² D _3/2-states were deduced: 3d ² D _3/2∶ ¦A¦=99(1) Me/sec · g_J/0,8,B/A=?0,22(12), ¦β¦=0.45 (8) Mc/sec/(kV/cm)² · g_J,/0.8, A/β< 0 3d²D_5/2∶ ¦β¦=0.16 (4) Mc/sec/(kV/cm)² · g_J/1.2, A/β>0. Some qualitative aspects of interconfiguration mixing in the 3d²D-states are discussed.     

Critical parameters near the ferromagnetic-paramagnetic phase transition in La0.7A0.3(Mn1−xbx)O3 (A=Sr; B=Ti and Al; x=0.0 and 0.05) compounds

The critical parameters provide important information concerning the interaction mechanisms near the paramagnetic-to-ferromagnetic transition. In this paper, we present a thorough study for the critical behavior of La_0.7A_0.3(Mn_1−xB_x)O₃ (A=Sr; B=Ti and Al; x=0.0 and 0.05) polycrystalline samples near ferromagnetic-paramagnetic phase transition temperature by analyzing isothermal magnetization data. We have analyzed our dc-magnetization data near the transition temperature with the help of the modified Arrot plot, Kouvel-Fisher method. We have determined the critical temperature T_C and the critical parameters β, γ and δ. With the values of T_C, β and γ, we plot M×(1−T/T_C)^−β vs. H×(1−T/T_C)^−γ. All the data collapse on one of the two curves. This suggests that the data below and above T_C obey scaling, following a single equation of state. Critical parameters for x=0 and x_Ti=0.05 samples are between those predicted for a 3D-Heisenberg model and mean-field theory and for x_Al=0.05 samples the values obtained for the critical parameters are close to those predicted by the mean-field theory.     

Der Einfluß eines elektrischen Feldes auf Level-Crossings des 6d 2 D 3/2-Zustands im TlI-Spektrum

The influence of an electric field on the energy levels of the 6d²D_3/2-state in the Tl I-spectrum was studied by measuring the shifts of level crossing signals relative to their magnetic field positions. The following values of the magnetic hyperfine constantA and the Stark parameterβ were deduced: ¦A¦=42(2) Mc/sec · g_J/0.8, ¦β¦=0.12(1) Mc/sec/(kV/cm)² · g_J/0.8 and A/β>0. Assuming that the main part of the energy shifts are caused by admixtures of the 7p²P-states the sign of the Stark parameterβ and —from the measured ratio A/β>0 —the sign of theA-factor should be negative. For electric field strength E?30 kV/cm the energy shifts of the 6d²D_3/2state are considerably greater than the hyperfine structure splitting. Therefore the case of decoupled hyperfine structure is considered.     

Higher order reggeon field theory results for dσ/dt

The critical reggeon field theory (RFT) asymptotic scaling law for dσ/dt can be evaluated using the ε expansion for renormalization group (RG) quaatities at t ≠ 0 along with the two variable RG equations found by Abarbanel, Bartels, Bronzan and Sidhu (ABBS). The amplitude thus obtained has an ε-exponentiated form. Interestingly, it reduces in a certain limit to the Bessel function pomeron model advocated by Kane. We perform a systematic numerical study here.Our results are as follows. Although the asymptotic RFT scaling is violated by the data, introduction of a mild external particle vertex with one parameter improvesthe situation considerably at current energies. Moreover, the shape of the ABBS scaling curve predicted by the O(ε²) results of Dash and Grandou is in at least qualitative agreement with the data, including the absence of a second dip. Two additional parameters (the t = 0 normalization and the scale in t) have to be fixed by hand.The overall conclusion is that in spite of many a priori objections the asymptotic RFT does a surprisingly good job of describing both the s and t dependence of dσ/dt at current energies.     

Luminescence study of the 4f5d configuration of Nd in LiYF4, LiLuF4 and BaY2F8 crystals

Ultraviolet fluorescence of Nd³⁺ ions induced by triphotonic excitation process was studied in Nd-doped LiYF₄, LiLuF₄ and BaY₂F₈ crystals using a technique of time-resolved spectroscopy. The observed ultraviolet luminescence was due to transitions between the bottom of 4f²5d configuration and 4f³ states of Nd³⁺ ions. Narrow emission lines superposed to the broadband emissions were observed. A detailed analysis of luminescence spectrum revealed that the narrow emissions are due to parity and spin allowed radiative transitions from the Stark levels of ⁴K_11/2(5d) state created by the electrostatic interaction between the 5d electron and the two electrons of the 4f² configuration. The narrow emissions are related to the high spin state (S=3/2) which gives f-f characteristics to the f-d broadband emissions. The narrow emissions superposed to the wide emission correspond to 18%, 34% and 43% of the integrated broadband emission at 262 nm observed in LiYF₄, LiLuF₄ and BaY₂F₈ crystals, respectively. Although the 5d-4f² interaction is observed to be weaker than 5d-crystal field interaction, it is stronger enough to select only the radiative transitions from 4f²5d configuration to 4f³ states that preserves the total spin S=3/2.     

Ab initio study of 5d-shells Ir substitution for Fe-based SmOFe1−xIrxAs

The lattice and electronic properties for 5d-shells Ir substituted Fe-based superconductor SmOFe_1−xIr_xAs (x=0,0.2,0.25,0.3) are investigated based on the density functional theory (DFT) with a spin generalized gradient approximation SGGA+U method. The electronic density of states (DOS) of SmOFe_1−xIr_xAs is studied and well compared with the results of experimental X-ray photoemission spectroscopy (XPS). The calculation indicated that iridium substitution at the Fe site induced a modification of the FeAs₄ tetrahedron and suppressed the magnetic ordering corresponding to the Fe-3d, which may be the main cause of inducing superconductivity in Ir-doped SmOFeAs system.     

Microwave spectrum, molecular structure, and theoretical calculation of cyclohexanone oxime (chair form)

The microwave spectra of cyclohexanone oxime and d₁ (=NOD) and d₄(2,2,6,6-d₄) derivatives were observed in the frequency range from 8 to 40 GHz in the ground and excited vibrational states. The rotational constants were determined to be A = 3799.844(48), B = 1513.7912(23), and C = 1189.6118(29) MHz for normal species, A = 3791.835(88), B = 1461.0324(47), and C = 1157.5653(53) MHz for d₁ species, and A = 3364.141(49), B = 1487.9551(34), and C = 1154.0965(44) MHz for d₄ species in the ground vibrational state. The planar moments, P_bb (P_bb = (I_c + I_a − I_b)/2) of normal, d₁, and d₄ species were determined to be 111.9885(26), 111.9817(46), and 124.2394(49) uŲ, respectively. The almost same values of P_bb of normal and d₁ species suggest that the hydroxyl hydrogen atom is very close to the a-c plane. From the r_s coordinates of the hydroxyl hydrogen atom, the OH bond was found to be at the trans position with respect to the CN double bond. The conformation of cyclohexanone oxime was determined to be chair form by comparing the observed and calculated rotational constants, ΔI, and planar moments, and taking account of the calculated the relative energy difference, ΔE. The structural parameters, the three bond lengths, three bond angles, and three dihedral angles, were adjusted to the nine rotational constants observed. The bond angle of ∠C₂C₁N is much wider than that of ∠C₆C₁N by about 10°. The dihedral angles of ∠C₁C₂C₃C₄, ∠C₂C₃C₄C₅, and ∠C₃C₄C₅C₆ were determined to be 53.3(5), −57.2(5), and 57.2(5)°. Two vibrational modes were assigned to the ring-bending and ring-twisting ones, which are almost harmonic up to v = 3.     

Canonical realizations of the lie algebras gl(n, R) and sl(n, R) I. Formulae and classification

The generators of the Lie algebra of the general linear group GL(n, R) and of the special linear group SL(n, R) are, recurrently, expressed through polynomials in the quantum canonical variables p_t and q_t. These realizations are skew-Hermitian, the Casimir operations are realized by constant multiples of identity element and, in dependence on the number of the canonical pairs used, they depend on d(d?1 for sl (n,R)), d = 2, …, n, free real parameters.     

Core excitons in solid rare gases: Kr-3d and Xe-4d transitions

Core excitons from 3d levels of Kr and 4d levels of Xe are examined within the integral equation formalism both in the isolated atoms and in the crystals. Earlier interpretation that resonances at the interband edge Kr-3d and Xe-4d are due to 1s, 2p, 3p excitons is well supported by the present calculation.     

The complete N =2, d = 10 supergravity

The alternative N = 2, d = 10 supergravity, which is not derivable by dimensional reduction from the N = 1, d = 11 theory, is constructed at the full non-linear level. The transformation laws of the component fields and the equations of motion are derived and shown to be consistent. The derivation makes use of superspace techniques and exploits the fact that the scalars belong to the coset space SU(1,1)/U(1).     

Resonanzstreuung von Licht in magnetischen und elektrischen Feldern zur Untersuchung der Hyperfeinstruktur des 7d 2 D 3/2-Terms im Thallium I-Spektrum

Observing the resonance fluorescence of the transition 7d ² D _3/2-6p ² P _1/2 (λ=2379 Å) in the Tl I-spectrum the level crossing technique with combined electric and magnetic fields was used to investigate the hyperfine structure and the Stark effect of the 7d ² D _3/2-state. For electric field strengthsE?25 kV/cm the Stark shifts are considerably greater than the hyperfine splitting. Therefore the crossing signals for the case of decoupled hyperfine structure could be detected. The following values of the magnetic hyperfine constantA and the Stark parameterβ were deduced: ¦A¦=55(1) Mc/sec·g _J /0.8, ¦β¦=0.20(4) Mc/sec/(kV/cm)²·g _J /0.8 andA/β>0. The widths of the signals yielded the mean lifetimeτ=2.7(5)·10^?8 sec· 0.8/g _J . Sign and values ofA andβ are discussed.     

Lambda polarization in inclusive K−p interactions at 10 and 16 GeV/c

A strong negative transverse polarization P_z is found for forward produced lambdas observed in 10 and 16 GeV/c K^?p interactions. This indicates that exchanges of natural spin-parity are dominant in the production process. Using the polarization results, the $\text{d}\text{σ}\text{d}\text{u′}$ distributions for natural and unnatural spin-parity exchanges are derived. For unnatural exchanges, a dip is observed at u′?0.3 GeV², which can be explained as a nonsense-wrong-signature zero of the N_β trajectory. The value of P_z for forward producted lambdas is constant with energy. This is in agreement with the triple-Regge model prediction, as is the fact that P_z is constant as a function of $\text{M}{}^2\text{s}$. The two non-transverse polarization components, P_x and P_y, have been measured and are found to be consistent with zero for all x values, unlike P_z.     

Stark-Effekt-Untersuchungen der Hyperfeinstruktur der 5s25d2D3/2- und 5s25d2D3/2-Terme im In I-Spektrum

The level-crossing technique with combined electric and magnetic fields was used to investigate the hyperfine structure of the 5s ²5d ² D _3/2- and 5s ²6d ² D _3/2-stedes of the In I-spectrum. From the shifts of the level-crossing signals due to the Stark effect of the electric field the Stark constantsβ of both states were deduced: 5s ²5d ² D _3/2: ¦β¦=0.33(3) Mc/(kV/cm)² 5s ²6d ² D _3/2: ¦β¦=6(1) Mc/(kV/cm)². By theoretical calculations with wave functions of the Coulomb approximation one can show, that the Stark effect in both states is mainly due to admixtures of the 5s ²6p- resp.5s ²7p-configuration.     

Temperature dependence of the energy gap of MgxZn1−xTe semiconductors alloys

Wavelength-modulation spectroscopy is used to obtain the temperature dependence of the near band gap reflectivity spectrum E_o of Mg_xZn_1?xTe ternary semiconducting alloys. Results are given in the range 80–100 K for the cubic materials: 0〈x〈0.5. The analysis of the line shapes as a function of x and T confirms the hypothesis of an exciton bound to the complex defect associated with zinc vacancy, as ZnTe. The E_o(x) curve is parabolic. The bowing parameter is C=0.45 ± 0.1 eV at 80 K, C=0.6 ± 0.1 eV at 300 K. Within experimental scattering the temperature coefficient dE₀dT is nearly constant with x:-4.5±0.3 × 10^?4eVK^?1. This data is smaller than the value calculated in the literature for ZnTe from pseudo potential method.     

Monte Carlo study of the critical behavior and magnetic properties of La2/3Ca1/3MnO3 thin films

Critical exponents offer important information concerning the interaction mechanisms near the paramagnetic to ferromagnetic transition. In this work a Monte Carlo-Metropolis simulation of the critical behavior in La_2/3Ca_1/3MnO₃ thin films is addressed. Canonical ensemble averages for magnetization per site, magnetic susceptibility and specific heat of stoichiometric manganite within a three-dimensional classical Heisenberg model with nearest magnetic neighbor interactions are computed. The La_2/3Ca_1/3MnO₃ thin films were simulated addressing the thickness influence and thermal dependence. In the model, Mn magnetic ions are distributed on a simple cubic lattice according to the perovskite structure of this manganite. Ferromagnetic coupling for the bonds Mn³⁺-Mn³⁺(e_g-e_g′), Mn³⁺-Mn⁴⁺(e_g-d³) and Mn³⁺-Mn⁴⁺(e_g′-d³) were taken into account. On the basis of finite-size scaling theory, our best estimates of critical exponents, linked to the ferromagnetic to paramagnetic transition, for the correlation length, specific heat, magnetization and susceptibility are, respectively: v=0.56±0.01, α=0.16±0.03, β=0.34±0.04γ and γ=1.17±0.05. These theoretical results are consistent with the Rushbrooke equalitiy α+2β+γ=2.     

Ab-initio calculations of Co-based diluted magnetic semiconductors Cd1−xCoxX (X=S, Se, Te)

Ab-initio calculations are performed to investigate the structural, electronic and magnetic properties of spin-polarized diluted magnetic semiconductors composed of II-VI compounds Cd_1−xCo_xX (X=S, Se, Te) at x=0.25. From the calculated results of band structure and density of states, the half-metallic character and stability of ferromagnetic state for Cd_1−xCo_xS, Cd_1−xCo_xSe and Cd_1−xCo_xTe alloys are determined. It is found that the tetrahedral crystal field gives rise to triple degeneracy t_2g and double degeneracy e_g. Furthermore, we predict the values of spin-exchange splitting energies Δ_x(d) and Δ_x(p−d) and exchange constants N₀α and N₀β produced by the Co 3d states. Calculated total magnetic moments and the robustness of half-metallicity of Cd_1−xCo_xX (X=S, Se, Te) with respect to the variation in lattice parameters are also discussed. We also extend our calculations to x=0.50, 0.75 for S compounds in order to observe the change due to increase in Co.     

Numerical investigation of natural convection heat transfer of nanofluids in a Γ shaped cavity

This paper analyzes the heat transfer and fluid flow of natural convection in a Γ shaped enclosure filled with Al₂O₃/Water nanofluid that operates under differentially heated walls. The Navier–Stokes and energy equations are solved numerically. Heat transfer and fluid flow are examined for parameters of non-uniform nanoparticle size, mean nanoparticle diameter, nanoparticle volume fraction, Grashof number and different geometry of enclosure. Finite volume method is used for discretizating positional expressions, and the forth order Rung-Kuta is used for discretizating time expressions. Also an artificial compressibility technique was applied to couple continuity to momentum equations. Results indicate that using nanofluid causes an increase in the heat transfer and the Nusselt number so that for R = 0.001 in Gr = 10³, the Nusselt number 25%, in Gr = 10⁴ 26%, and in Gr = 10⁵ 28% increases. Furthermore; by decreasing the mean diameters of nanoparticles, Nusselt number increases. By increasing R parameter (d_p,min/d_p,max) and nano particle volume fraction, Nusselt number increases.