Counting BPS operators in SYM

The free field partition function for a generic U(N) gauge theory, where the fundamental fields transform in the adjoint representation, is analysed in terms of symmetric polynomial techniques. It is shown by these means how this is related to the cycle polynomial for the symmetric group and how the large N result may be easily recovered. Higher order corrections for finite N are also discussed in terms of symmetric group characters. For finite N, the partition function involving a single bosonic fundamental field is recovered and explicit counting of multi-trace quarter BPS operators in free super-Yang–Mills discussed, including a general result for large N. The partition function for quarter BPS operators in the chiral ring of super-Yang–Mills is analysed in terms of plane partitions. Asymptotic counting of BPS primary operators with differing R-symmetry charges is discussed in both free super-Yang–Mills and in the chiral ring. Also, general and explicit expressions are derived for SU(2) gauge theory partition functions, when the fundamental fields transform in the adjoint, for free field theory.     

High-power continuous-wave operation of a diode-pumped laser at

The continuous-wave laser properties of an efficient diode-pumped Nd:GdVO₄ crystal operating at formed with a simple plane-concave cavity have been studied. With the incident pump power of 21 W, an output power of 6.9 W was obtained, giving an optical conversion efficiency of 32.8% and a slope efficiency of 35.3%. The laser characterization of two different Nd³⁺-doped concentration of Nd:GdVO₄ crystals were studied.     

Fabrication of polyaniline/ heterojunction structure using plasma enhanced polymerization technique

The work reports on the fabrication of a p–n heterojunction structure comprised of polyaniline (PANI) and TiO₂ nanoparticles. PANI was deposited by plasma enhanced polymerization on TiO₂ thin film substrates. The structural and the crystalline properties demonstrated the coherence and the substantive interaction of the plasma polymerized PANI molecules with the TiO₂ nanoparticle thin film. The UV–Vis studies of PANI/TiO₂ thin film supported the internalization of PANI with TiO₂ nanoparticles due to π–π^* transition of the phenyl rings with the lone pair electrons () of the nitrogen atom present in the PANI molecules. The I–V characteristics of the PANI/TiO₂ heterojunction structure were obtained in the forward and the reverse biased at applied voltage ranging from −1 V to +1 V with a scan rate of 2 mV/s. The proficient current in the PANI/TiO₂ heterojunction structure was attributed to the well penetration of PANI molecules into the pores of the TiO₂ nanoparticle thin film. The I–V characteristics ensured an efficient charge movement at the junction of PANI/TiO₂ interface and thus, behaved as a typical ohmic system.     

Tree-level contributions to the rare decays , , and in the Standard Model

The tree-level contributions to the rare decays , , and are analyzed and compared to those occurring in , , and . It is shown that these purely long-distance contributions, arising from the exchange of a charged lepton, can be significant in B⁺ decays for an intermediate τ, potentially blurring the distinction between the modes used to extract B⁺→τ⁺ν_τ and those used to probe the genuine short-distance and FCNC transitions. Numerically, the tree-level contributions are found to account for 98%, 12% and 14% of the total , , and rates, respectively.     

The H2+ molecular ion: Low-lying states

Matching for a wavefunction the WKB expansion at large distances and Taylor expansion at small distances leads to a compact, few-parametric uniform approximation found in Turbiner and Olivares-Pilon (2011). The ten low-lying eigenstates of H₂⁺ of the quantum numbers (n,m,Λ,±)$(n,m,\Lambda ,\pm )$  with n=m=0$n=m=0$ at Λ=0,1,2$\Lambda =0,1,2$, with n=1$n=1$, m=0$m=0$ and n=0$n=0$, m=1$m=1$ at Λ=0$\Lambda =0$ of both parities are explored for all interproton distances R$R$. For all these states this approximation provides the relative accuracy ?10⁻⁵$?10^{-5}$ (not less than 5 s.d.) locally, for any real coordinate x$x$ in eigenfunctions, when for total energy E(R)$E\left(R\right)$ it gives 10-11 s.d. for R∈[0,50]$R\in [0,50]$  a.u. Corrections to the approximation are evaluated in the specially-designed, convergent perturbation theory. Separation constants are found with not less than 8 s.d. The oscillator strength for the electric dipole transitions E1$E1$ is calculated with not less than 6 s.d. A dramatic dip in the E1$E1$ oscillator strength f_{1sσg−3pσu}$f_{1s{\sigma }_g-3p{\sigma }_u}$ at R∼R_eq$R\sim R_{eq}$ is observed. The magnetic dipole and electric quadrupole transitions are calculated for the first time with not less than 6 s.d. in oscillator strength. For two lowest states (0,0,0,±)$(0,0,0,\pm )$ (or, equivalently, 1sσ_g$1s{\sigma }_g$ and 2pσ_u$2p{\sigma }_u$ states) the potential curves are checked and confirmed in the Lagrange mesh method within 12 s.d. Based on them the Energy Gap between 1sσ_g$1s{\sigma }_g$ and 2pσ_u$2p{\sigma }_u$ potential curves is approximated with modified Pade Re^−R[Pade(8/7)](R)$R{e}^{-R}\left[Pade(8/7)\right]\left(R\right)$ with not less than 4-5 figures at R∈[0,40]$R\in [0,40]$ a.u. Sum of potential curves E_1sσg+E_2pσu$E_{1s{\sigma }_g}+E_{2p{\sigma }_u}$ is approximated by Pade 1/R[Pade(5/8)](R)$1/R\left[Pade(5/8)\right]\left(R\right)$ in R∈[0,40]$R\in [0,40]$ a.u. with not less than 3-4 figures.     

Spherical-separability of Non-Hermitian Hamiltonians and Pseudo- PT\mathcal{PT} -symmetry

Non-Hermitian but -symmetrized spherically-separable Dirac and Schr?dinger Hamiltonians are considered. It is observed that the descendant Hamiltonians H _r , H _θ , and H _φ play essential roles and offer some “user-feriendly” options as to which one (or ones) of them is (or are) non-Hermitian. Considering a -symmetrized H _φ , we have shown that the conventional Dirac (relativistic) and Schr?dinger (non-relativistic) energy eigenvalues are recoverable. We have also witnessed an unavoidable change in the azimuthal part of the general wavefunction. Moreover, setting a possible interaction V(θ)≠0 in the descendant Hamiltonian H _θ would manifest a change in the angular θ-dependent part of the general solution too. Whilst some -symmetrized H _φ Hamiltonians are considered, a recipe to keep the regular magnetic quantum number m, as defined in the regular traditional Hermitian settings, is suggested. Hamiltonians possess properties similar to the -symmetric ones (here the non-Hermitian -symmetric Hamiltonians) are nicknamed as pseudo- -symmetric.     

Some observations related to intermittency and multifractality in Si and C-nucleus collisions at

An attempt is made to study the existence of dynamical fluctuations of relativistic particles using the methods of modified multifractal moments, G_q, and scaled factorial moments, F_q, in terms of new scaled variable X(η) suggested by Bialas and Gazdzicki. For this purpose analyses of experimental and UrQMD data involving interactions of ²⁸Si and ¹²C nuclei at with nuclear emulsion are used. The variation of lnG_q and lnF_q with lnM in pseudorapidity (η) phase space reveals power law behaviour. The values of slopes, τ_q and _q determined from the analyses of G_q and F_q moments are discussed. The generalized fractal dimensions, D_q, determined from the above methods are found to decrease with the order of the moments, q, indicating multifractality in multiparticle production. It is also observed that the spectral function f(α_q) for heavier projectile is much broader than for lighter beam due to larger number of participating nucleons present in heavier projectile.     

: A quantitative measure of NMR signal receiving efficiency

Recognizing that the sensitivity of NMR is influenced by factors such as conductance and dielectric constant of the sample, we propose the receiving efficiency to characterize how efficiently the NMR signal can be observed from a unit transverse magnetization in a sample under optimal probe tuning and matching conditions. Conveniently, the relative receiving efficiency can be defined as the ratio of the NMR signal induced by a unit transverse magnetization in a sample of interest and a reference solution. Based on the reciprocal relationship between excitation and observation in NMR, the relative receiving efficiency can be correlated with the 90° pulse length (τ₉₀). In the special case of perfect probe tuning (impedance matched to 50 Ω), is inversely proportional to τ₉₀. Application of the NMR receiving efficiency in quantitative analysis potentially enables a single external concentration reference for almost any sample, eliminating the need to know its exact chemical composition or detailed electromagnetic properties.     

First-principles calculations on elasticity of under pressure

First-principles calculations of the crystal structure and the elastic properties of OsN₂ have been carried out with the plane-wave pseudopotential density functional theory method. The calculated values are in very good agreement with experimental data as well as with some of the existing model calculations. The dependence of the elastic constants c_ij, the aggregate elastic moduli (B,G,E), Poisson’s ratio, and the elastic anisotropy on pressure has been investigated. Moreover, the variation of the Debye temperature and the compressional and shear elastic wave velocities with pressure P up to 60 GPa at 0 K have been investigated for the first time.     

Universal rise of hadronic total cross sections based on forward πp and scatterings

Recently there are several evidences of the increase of the total cross section σ_tot to be log²s consistent with the Froissart unitarity bound, and the COMPETE collaborations in the PDG have further assumed σ_totBlog²(s/s₀) to extend its universal rise with a common value of B for all the hadronic scatterings. However, there is no rigorous proof yet based only on QCD. Therefore, it is worthwhile to prove this universal rise of σ_tot even empirically. In this Letter we attempt to obtain the value of B for πp scattering, B_πp, with reasonable accuracy by taking into account the rich πp data in all the energy regions. We use the finite-energy sum rule (FESR) expressed in terms of the πp scattering data in the low and intermediate energies as a constraint between high-energy parameters. We then have searched for the simultaneous best fit to the σ_tot and ρ ratios, the ratios of the real to imaginary parts of the forward scattering amplitudes. The lower energy data are included in the integral of FESR, the more precisely determined is the non-leading term such as logs, and then helps to determine the leading terms like log²s. We have derived the value of B_πp as B_πp=0.311±0.044 mb. This value is to be compared with the value of B for scattering, B_pp, in our previous analysis [M. Ishida, K. Igi, Eur. Phys. J. C 52 (2007) 357], B_pp=0.289±0.023 mb. Thus, our result appears to support the universality hypothesis.     

Stopping power measurements of Si in polycarbonate detectors

The rate of energy loss of the impinging ion as it passes through succeeding layers of the target material gives information regarding the nature of the material and helps to calculate the range of the ions in a thick target in which the ions are stopped. In the present work, the range of 118 MeV ²⁸Si was measured in different types of polycarbonates, viz. Makrofol-N, Makrofol-G and Makrofol-KG, using the nuclear track technique. Polyallyldiglycol carbonate (PADC) was used as the backing detector. The experimental values of range and energy-loss rate are compared with the theoretical values obtained from different computer codes, viz. BENTON, HUBERT, RANGE, TRIM’98 and SRIM’03.     

Sectoral sampling in centric-scan SPRITE magnetic resonance imaging

A new approach to the construction of k-space trajectories for centric-scan SPRITE in both 2D and 3D is presented. All benefits of previous SPRITE methods are retained, most importantly the ability to image objects with short T*(2). This new approach gives more flexibility in the choice of number of interleaves with points more evenly distributed across k-space. All these improvements positively contribute to image quality and resolution, which can be also traded off against experimental speed. Sectoral sampling will have significant benefits for magnetisation preparation contrast imaging.     

Optical properties and g factors of GaAs quantum rods

The Hamiltonian of the zinc-blende quantum rods in the framework of eight-band effective-mass approximation in the presence of external homogeneous magnetic field is given. The electronic structure, optical properties and electron g factors of GaAs quantum rods are investigated. We found that the electron g factors are very sensitively dependent on the dimensions of the quantum rods. As some of the three dimensions increase, the electron g factors decrease. The more the dimensions increase, the more the electron g factors decrease. The dimensions perpendicular to the direction of the magnetic field affect the electron g factors more than the other dimension.     

Molecular dynamics study of structural changes in freezing clusters

Structural changes of Cu₅₁–Cu₅₆ clusters during freezing have been studied by employing molecular dynamics(MD) simulations. With the growth of the crystallization phase, local patterns in different regions determined by the atom density profiles present different characteristic for these studied clusters. While the atom movements in the even-number clusters result in the formation of initial two-shell, then three-shell, and finally four-shell structures, the atoms in the odd-number clusters, with one exception of the Cu₅₁ cluster, first move into the central region and the outermost parts, then follow the movement from the inner parts into the outer parts. The crystallization temperature of these clusters has an oscillatory increase behavior for odd- and even- numbered copper atoms with increasing cluster size.