Density functional study of $$\hbox {AgScO}_2$$: Electronic and optical properties

Dielectric relaxation studies of binary (jk) polar mixtures of tetrahydrofuran with N-methyl acetamide, N,N-dimethyl acetamide, N-methyl formamide and N,N-dimethyl formamide dissolved in benzene(i) for different weight fractions (w _{j k} ’s) of the polar solutes and mole fractions (x _j ’s) of tetrahydrofuran at 25 ^°C are attempted by measuring the conductivity of the solution under 9.90 GHz electric field using Debye theory. The estimated relaxation time (τ _{j k} ’s) and dipole moment (μ _{j k} ’s) agree well with the reported values signifying the validity of the proposed methods. Structural and associational aspects are predicted from the plot of τ _{j k} and μ _{j k} against x _j of tetrahydrofuran to arrive at solute–solute (dimer) molecular association upto x _j =0.3 of tetrahydrofuran and thereafter solute–solvent (monomer) molecular association upto x _j =1.0 for all systems except tetrahydrofuran + N,N-dimethyl acetamide.     

Anomalous dimensions of the Wilson operators in $$ \mathcal{N} $$ = 4 supersymmetric Yang-Mills theory

We present results for the universal anomalous dimension γ _uni(j) of Wilson twist-2 operators in the = 4 supersymmetric Yang-Mills theory in the first four orders of perturbation theory. The text was submitted by the authors in English.     

Singlet $$\tilde V$$ correlator within the instanton vacuum model

The correlator of singlet axial-vector and vector currents in the external electromagnetic field is studied within the instanton liquid model of the QCD vacuum. In the chiral limit, we calculate the longitudinal w _L ⁽⁰⁾ and transversal w _T ⁽⁰⁾ , with respect to the axial-vector index, invariant amplitudes at an arbitrary spacelike momentum transfer q. It is demonstrated how the anomalous longitudinal part of the correlator is renormalized at low momenta due to the presence of the U _A (1) anomaly.     

Some Families of the Incomplete H-Functions and the Incomplete $$\overline H $$ -Functions and Associated Integral Transforms and Operators of Fractional Calculus with Applications

Our present investigation is inspired by the recent interesting extensions (by Srivastava et al. [35]) of a pair of the Mellin–Barnes type contour integral representations of their incomplete generalized hypergeometric functions _p γ _q and _p Γ _q by means of the incomplete gamma functions γ(s, x) and Γ(s, x). Here, in this sequel, we introduce a family of the relatively more general incomplete H-functions γ _p,q ^m,n (z) and Γ _p,q ^m,n (z) as well as their such special cases as the incomplete Fox-Wright generalized hypergeometric functions _p Ψ _q ^(γ) [z] and _p Ψ _q ^(Γ) [z]. The main object of this paper is to study and investigate several interesting properties of these incomplete H-functions, including (for example) decomposition and reduction formulas, derivative formulas, various integral transforms, computational representations, and so on. We apply some substantially general Riemann–Liouville and Weyl type fractional integral operators to each of these incomplete H-functions. We indicate the easilyderivable extensions of the results presented here that hold for the corresponding incomplete \(\overline H \)-functions as well. Potential applications of many of these incomplete special functions involving (for example) probability theory are also indicated.     

Calculation of the fine structure of the triplet state $$\tilde a^3 A_2 $$ of the ozone molecule by the method of multiconfiguration self-consistent field

The zero-field splitting of the \(\tilde a^3 A_2 \) state of the O₃ molecule is interpreted on the basis of ab initio quantum-chemical calculations. The spin—orbit coupling with the ground X¹A₁ state is shown to make the main contribution to the zero-field splitting of the \(\tilde a^3 A_2 \) term (the state of the ³σπ type). The calculated parameters D and E agree well with experiment.     

Local-field anisotropy in cholesteric liquid crystals

The first experimental values of the Lorentz tensor components L _j for the cholesteric and smectic A phases of derivatives of cholesterol have been obtained using the dispersion of the refractive indices in the visible range. The temperature dependence of the components L _j has been determined; it is invariant with respect to the cholesteric-smectic A phase transition. The effect of the isotropization of the Lorentz and local field tensors with decreasing anisotropy of the molecular polarizability has been revealed.     

The four-loop anomalous dimension of the Konishi operator in $$ \mathcal{N} $$ = 4 Supersymmetric Yang-Mills theory

We present the result of a full direct component calculation for the planar four-loop anomalous dimension of the Konishi operator in = 4 Supersymmetric Yang-Mills theory. Our result confirms the results obtained from superfield and superstring computations, which take into account finite size corrections to the all-loop asymptotic Bethe ansatz for the integrable models describing the spectrum of the anomalous dimensions of the gaugeinvariant operators and the spectrum of the string states in the framework of the gauge/string duality. The article is published in the original.     

On the possibility of laser generation without inversion on the fine-structure levels of a helium atom

It is shown that laser generation is possible in principle upon coherent excitation according to the V-scheme of the (1s2p)³ P _j levels with j = 1, 2 of a helium atom from the (1s2s)³ S ₁ level of the same atom when the latter level is, in turn, populated by electron or proton impact.     

The effect of the nonplanarity of heterocyclic analogues of fluorene with the phosphorus atom on spin-orbit interactions

The transition dipole moments P ₀₀ ^S for the transitions from the sublevels s=z,y, and x of the triplet electronic states ³ A″, which are caused by intramolecular spin-orbit (SO) interactions, are calculated. The calculation is carried out for molecules of heterocyclic analogues of fluorene containing phosphorus and nitrogen (namely, the groups P-H, P-C₆H₅, and N-H). The influence that the planar and nonplanar models of the molecules, as well as the substituents ?C₆H₅ and ?H at the heteroatom (HA), exert on the values of (P ₀₀ ^S )² and on the directions of the corresponding vectors is considered. The values of the component \(k_{SO^ \sim } \sum _s (P_{00}^s )^2 \) of the radiative deactivation rate constant of the T ₁ state are calculated. It is ascertained that, in the series of molecules with HA = N, O, P, and S, both the calculated values of k _SO and those experimentally determined from an analysis of the intensity distribution in fine-structure phosphorescence spectra vary little, whereas the constant of the SO coupling in the heteroatom ?_HA increases substantially along this series. The reason for the weak influence of ?_HA on values of k _SO—common for both planar and nonplanar molecules—is found.     

Vector correlations in the F + HD reaction

A theoretical study of the orientation of product rotational angular momenta for two chemical reaction channels: F + HD(ν _r = 0, j _r = 0) → HF(ν, j) + D and F + HD(ν _r = 0, j _r = 0) → DF(ν, j) + H at a E _coll = 78.54 meV collision energy was performed. Angular momentum orientation was described on the basis of irreducible tensor operators (state multipoles) expressed through anisotropy transfer coefficients, which contained quantum-mechanical scattering T matrices determined on the basis of exact solutions to quantum scattering equations obtained using the hyperquantization algorithm. The possibility of the existence of substantial orientation of the angular momentum of reaction products j in the direction perpendicular to the scattering plane was demonstrated. The dependences of differential reaction cross sections and state multi-poles on the ν and j quantum numbers were calculated and analyzed. A experimental scheme based on the multiphoton ionization method was suggested. The scheme can be used to detect predicted reaction product angular momentum orientation.     

Fluctuations for the Ginzburg-Landau $${\nabla \phi}$$ Interface Model on a Bounded Domain

We study the massless field on \({D_n = D \cap \tfrac{1}{n} \mathbf{Z}^2}\), where \({D \subseteq \mathbf{R}^2}\) is a bounded domain with smooth boundary, with Hamiltonian \({\mathcal {H}(h) = \sum_{x \sim y} \mathcal {V}(h(x) - h(y))}\). The interaction \({\mathcal {V}}\) is assumed to be symmetric and uniformly convex. This is a general model for a (2 + 1)-dimensional effective interface where h represents the height. We take our boundary conditions to be a continuous perturbation of a macroscopic tilt: h(x) = n x · u + f(x) for \({x \in \partial D_n,\,u \in \mathbf{R}^2}\), and f : R ² → R continuous. We prove that the fluctuations of linear functionals of h(x) about the tilt converge in the limit to a Gaussian free field on D, the standard Gaussian with respect to the weighted Dirichlet inner product \({(f,g)_\nabla^\beta = \int_D \sum_i \beta_i \partial_i f_i \partial_i g_i}\) for some explicit β = β(u). In a subsequent article, we will employ the tools developed here to resolve a conjecture of Sheffield that the zero contour lines of h are asymptotically described by SLE(4), a conformally invariant random curve.     

Spectral and Scattering Theory of Space-cutoff Charged $${P(\varphi)_{2}}$$ Models

We consider in this paper space-cutoff charged \({P(\varphi)_{2}}\) models arising from the quantization of the non-linear charged Klein–Gordon equation:

$(\partial_{t}+\i V(x))^{2}\phi(t, x)+ (-\Delta_{x}+ m^{2})\phi(t,x)+ g(x)\partial_{\overline{z}}P(\phi(t,x), \overline{\phi}(t,x))=0,$

where V(x) is an electrostatic potential, g(x) ≥ 0 a space-cutoff, and \({P(\lambda, \overline{\lambda})}\) a real bounded below polynomial. We discuss various ways to quantize this equation, starting from different CCR representations. After describing the construction of the interacting Hamiltonian H we study its spectral and scattering theory. We describe the essential spectrum of H, prove the existence of asymptotic fields and of wave operators, and finally prove the asymptotic completeness of wave operators. These results are similar to the case when V = 0.

     

Integral characteristics of vibronic-spin-orbit interactions in a phosphorus-containing analogue of the fluorene molecule

The strengths (P ₀₀ ^s )² and F _VSO ² of the transitions from the triplet sublevels s = z, y, and x of the electronic state ³A″ of the phenyldibenzophosphole (DB(P-Ph)) molecule are calculated taking into account the intramolecular spin-orbit (SO) and joint vibronic-spin-orbit (VSO) interactions. The contributions to the vibronic transition strengths from the SO interactions in different structural elements of the molecule (the C atoms of the dibenzene framework, the P atom, and the Ph substituent) are determined. The effect of the nonplanar nuclear configuration of the DB(P-Ph) molecule on the values of F _VSO ^s is investigated. The radiative deactivation rate constants of the k _rad ^s triplet sublevels T ^s are estimated. It is found that the vibrations of the A′(B₁) symmetry in the fine-structure phosphorescence spectrum of DB(P-Ph) occur due to both the SO coupling exclusively in the P atom and the T ^x → S₀ transition (the x axis is perpendicular to the planar dibenzene framework of the molecule) with a high (preferential) population of this triplet sublevel.     

Genesis of the anomalous Hall effect in CeAl<Subscript>2</Subscript>

The Hall coefficient R _H , resistivity ρ, and Seebeck coefficient S of the CeAl₂ compound with fast electron density fluctuations were studied in a wide temperature range (from 1.8 to 300 K). Detailed measurements of the angular dependences R _H (? T, H≤70 kOe) were performed to determine contributions to the anomalous Hall effect and study the behavior of the anomalous magnetic R _H ^am and main R _H ^a components of the Hall signal of this compound with strong electron correlation. The special features of the behavior of the anomalous magnetic component R _H ^am were used to analyze the complex magnetic phase diagram H-T determined by magnetic ordering in the presence of strong spin fluctuations. An analysis of changes in the main contribution R _H ^a (H, T) to the Hall effect made it possible to determine the complex activation behavior of this anomalous component in the CeAl₂ intermetallic compound. The results led us to conclude that taking into account spin-polaron effects was necessary and that the Kondo lattice and skew-scattering models were of very limited applicability as methods for describing the low-temperature transport of charge carriers in cerium-based intermetallic compounds. The effective masses and localization radii of manybody states in the CeAl₂ matrix were estimated to be (55–90)m₀ and 6–10 Å, respectively. The behaviors of the parameters R _H , S, and ρ were jointly analyzed. The results allowed us to consistently describe the transport coefficients of CeAl₂.     

Phase transition in the vortex structure of granular YBa<Subscript>2</Subscript>Cu<Subscript>3</Subscript>O<Subscript>7 − δ</Subscript> HTSCs in weak magnetic fields

This study aims at establishing the interrelation between the current-carrying capacity and peculiarities of magnetoresistance of granular YBa₂Cu₃O_{7 ? δ} HTSCs (T _c = 92.5 K). The transverse magnetoresistance of several batches of YBa₂Cu₃O_{7 ? δ} HTSC samples with noticeably different values of critical supercurrent density j _c is measured in magnetic fields H _ext up to H _ext ^max ≈ 500 Oe in a wide range of transport currents (5 mA ≤ I ≤ 1600 mA) at T = 77.4 K. Samples with relatively high values of j _c (H _ext = 0) ≥ 100 A/cm² do not exhibit any anomalies in their field dependences. Magnetoresistance jumps δρ_BG-VG/ρ_273K are observed for samples with low values of j _c ≥ 20 A/cm² in fields H _BG-VG ≈ 200–260 Oe. The width ΔH _BG-VG of the anomalous resistance region increases upon an increase in I. The magnetoresistance jumps decrease with increasing I in increasing field H _ext(0 → H _ext ^max ) and increase in decreasing field H _ext(H _ext ^max → 0). It is found that these peculiarities of the field dependences of magnetoresistance are associated with a first-order phase transition (in magnetic field) in the vortex structure of YBa₂Cu₃O_{7 ? δ} HTSCs of the Bragg glass-vortex glass type.     

A Minkowski Type Trace Inequality and Strong Subadditivity of Quantum Entropy II: Convexity and Concavity

We revisit and prove some convexity inequalities for trace functions conjectured in this paper’s antecedent. The main functional considered is

$ \Phi_{p,q} (A_1,\, A_2, \ldots, A_m) = \left({\rm Tr}\left[\left( \, {\sum\limits_{j=1}^m A_j^p } \, \right) ^{q/p} \right] \right)^{1/q} $

for m positive definite operators A _j . In our earlier paper, we only considered the case q = 1 and proved the concavity of Φ _p,1 for 0 < p ≤ 1 and the convexity for p = 2. We conjectured the convexity of Φ _p,1 for 1 < p < 2. Here we not only settle the unresolved case of joint convexity for 1 ≤ p ≤ 2, we are also able to include the parameter q ≥ 1 and still retain the convexity. Among other things this leads to a definition of an L ^q (L ^p ) norm for operators when 1 ≤ p ≤ 2 and a Minkowski inequality for operators on a tensor product of three Hilbert spaces – which leads to another proof of strong subadditivity of entropy. We also prove convexity/concavity properties of some other, related functionals.

     

Refinement of the hadronic contribution to the muon anomalous magnetic moment and to α(<Emphasis Type="Italic">M</Emphasis><Stack><Subscript>z</Subscript><Superscript>2</Superscript></Stack>)

The contribution of the muon anomalous magnetic moment aμ(hadr) to the vacuum polarization and electro-magnetic coupling constant α(q²) for q²=M _z ² is refined by using a new, more accurate value of the ρ-meson width. The values aμ(hadr)=678(7)×10^?10 and δα(M _z ² =0.02786(6) were obtained in a QCD model with an infinite number of vector mesons.