Refractive indices of biaxial crystals evaluated from the refractive indices ellipsoid equation

The expressions of the refractive indices corresponding wave vector k(θ,) are given by using coordinate transformations for the refractive indices ellipsoid equation of biaxial crystals. The refractive index expression of the wave, whose velocity is slower, is given by

and that of the wave, whose velocity is faster, is given by

     

Anomalous dimension with wrapping at four loops in SYM

In this paper we give all the details of the calculation that we presented in our previous paper [F. Fiamberti, A. Santambrogio, C. Sieg, D. Zanon, Wrapping at four loops in SYM, arXiv: 0712.3522], concerning the four-loop anomalous dimension of the Konishi descendant tr(ZZ−ZZ) in the SU(2) sector of the planar SYM theory. We explicitly consider all the wrapping diagrams that we compute using an superspace approach and Gegenbauer polynomial x-space techniques.     

Theoretical structure and surface energy of the reconstructed {01.2} form of calcite (CaCO3) crystal

Two different reconstructions of the (01.2) face (Ca or CO₃ terminated) of calcite (CaCO₃) were studied: (i) R1 reconstruction: the outermost layer is based on the [0 1 0] × 1/3[2 1 1] rectangular mesh, which is symmetrical with respect to the c glide plane of the crystal, thus fulfilling the 2D symmetry of the face and (ii) R2 reconstruction: the outermost layer is based on a lozenge shaped mesh that does not respect the 2D symmetry of the face.The , , and slabs geometry optimizations of calcite (CaCO₃) were performed either at DFT level or by using empirical potentials; the results obtained with these two different calculation methodologies are in good agreement. With respect to their arrangement in the bulk, the CO₃ groups of the outermost layer are significantly rotated about the crystallographic a-axis and about the normal to the 01.2 plane; further, the thickness of the outermost layer is significantly lower than that of the underneath ones.The surfaces energies (γ) at 0 K, for relaxed and unrelaxed , , and faces, were determined either at DFT level or by using empirical potentials. Independently of the method of calculation employed, the stability order of the relaxed faces is < < < . Concerning the unrelaxed faces, whose energies were evaluated by using empirical potentials only, the stability order is instead < < < ; such different ordering shows the importance of geometry relaxation in the calculation of the surface energy. The values of the relaxed surface energies are , , and erg/cm².     

Structure of light hypernuclei

The structure of light hypernuclei with strangeness S=−1 and −2 is investigated with the microscopic cluster model and the Gaussian expansion method (GEM). We emphasize that the cluster picture as well as the mean-field picture is invaluable to understand the structure of Λ hypernuclei, Σ hypernuclei and double Λ hypernuclei. A variety of aspects of Λ hypernuclei is demonstrated through a systematic study of p-shell hypernuclei (,, , , , , ) and sd-shell ones (, ): for example, the appearance of genuine hypernuclear states with new spatial symmetry which cannot be seen in ordinary nuclei, the glue-like role of the Λ particle which shrinks the size of nuclear core and thus reduces the B(E2) value, and the halo and skin structures in and etc. The typical light hypernucleus is thoroughly investigated, including its production, structure and decay. Precise three-body and four-body calculations of , and using GEM provide important information on the spin structure of the underlying ΛN interaction, by comparing with recent experimental data from γ-ray hypernuclear spectroscopy. The Λ–Σ coupling effect is studied in and . The binding mechanism of is discussed together with the possible existence of , emphasizing the fact that the study of is useful for extracting information on the ΣN interaction differing from that from . A systematic study of double-Λ hypernuclei, constrained by the NAGARA data () within a four-body cluster model indicates that the recently observed Demachi–Yanagi event can be interpreted as the 2⁺ state of . The effect of hyperon mixing in and is investigated using one-boson-exchange potentials and quark-cluster-model interactions for the S=−2 sector. A close relation between nuclear deep hole states and hypernuclei is discussed, emphasizing the selection rule for fragmentation of the s-hole in light nuclei, which is promising for understanding the production mechanism of double-Λ and twin-Λ hypernuclei via Ξ-atomic capture.     

Critical Casimir amplitudes for n-component models with -symmetry breaking quadratic boundary terms

Euclidean n-component ⁴ theories whose Hamiltonians are O(n) symmetric except for quadratic symmetry breaking boundary terms are studied in the film geometry . The boundary terms imply the Robin boundary conditions at the boundary planes at z=0 and at z=L. Particular attention is paid to the cases in which m_j of the n variables associated with plane take the special value corresponding to critical enhancement while the remaining ones are larger and hence subcritically enhanced. Under these conditions, the semi-infinite system with boundary plane has a multicritical surface–bulk point, called m_j-special, at which an O(m_j) symmetric critical surface phase coexists with the O(n) symmetric bulk phase, provided d is sufficiently large. The L-dependent part of the reduced free energy per cross-section area behaves asymptotically as Δ_C/L^d−1 as L→∞ at the bulk critical point. The Casimir amplitudes Δ_C are determined for small =4−d in the general case where m_c,c components _α are critically enhanced at both boundary planes, m_c,D+m_D,c components are enhanced at one plane but satisfy asymptotic Dirichlet boundary conditions at the respective other, and the remaining m_D,D components satisfy asymptotic Dirichlet boundary conditions at both . Whenever m_c,c>0, the corresponding small- expansions involve, besides integer powers of , also fractional powers ^k/2 with k3 modulo powers of logarithms. Results to order ^3/2 are given for general values of m_c,c, m_c,D+m_D,c, and m_D,D. These are used to estimate the Casimir amplitudes Δ_C of the three-dimensional Heisenberg systems with surface spin anisotropies for the cases with (m_c,c,m_c,D+m_D,c)=(1,0), (0,1), and (1,1).     

Asymmetric di-jet production in polarized hadronic collisions

Using the collinear QCD factorization approach, we study the single-transverse-spin dependent cross section Δσ(S) for the hadronic production of two jets of momenta P₁=P+q/2 and P₂=−P+q/2. We consider the kinematic region where the transverse components of the momentum vectors satisfy PqΛ_QCD. For the case of initial-state gluon radiation, we show that at the leading power in q/P and at the lowest non-trivial perturbative order, the dependence of Δσ(S) on q decouples from that on P, so that the cross section can be factorized into a hard part that is a function only of the single scale P, and into perturbatively generated transverse-momentum dependent (TMD) parton distributions with transverse momenta .     

Magnetostructural phase transitions of DyFe4Ge2: Part II Neutron diffraction

We present the temperature magnetic phase diagram of the compound DyFe₄Ge₂ determined from neutron diffraction data for the entire magnetically ordered regime. DyFe₄Ge₂ undergoes at a simultaneous structural and magnetic transition of second order (or weakly first order) followed by two subsequent isostructural first-order magnetic transitions at and T_ic1=28K:

The re-entrant lock-in magnetic phase is stable in the high-temperature range T_ic2–T_N and in the low-temperature range 1.5 K–T_ic1 while the incommensurately modulated magnetic phase is sandwiched in the intermediate range T_ic1–T_ic2 between the two commensurate phases. The wave vector q₂ has a temperature-dependent length with a minimum in the middle of the incommensurate range and corresponds to a multiaxial amplitude modulated phase. Symmetry analysis leads for both propagation vectors in Cmmm to a twofold and fourfold splitting of the tetragonal Dy 2b site and the Fe 8i sites, respectively. The low temperature and the phases correspond to 3D canted magnetic structures described by the irreducible representations (Irreps) Γ₂+Γ₃ while the high-temperature q₁ phase to 2D canted magnetic structures described by a single Irrep Γ₂. The T_ic2 transition is connected with reorientations of both Fe and Dy moments.     

Unfamiliar integrals and motions down the ‘plug-hole’ potential

The orbits in the potentials ψ=−CzR⁻²+ζ(R), (ζ arbitrary) have integrals E, and . Thus the z-velocity is proportional to the number of turns made around the axis! The Poisson Bracket [h,I] is not zero so Liouville’s integrability theorem does not apply. Starting from the self-similar potential with ζ∝R⁻¹, we find some orbits that spiral around cones and explore general orbits in this strange system.     

Low mass dilepton production at ultrarelativistic energies

Dilepton production in pp and Au+Au nucleus–nucleus collisions at as well as in In+In and Pb+Au at is studied within the microscopic HSD transport approach. A comparison to the data from the PHENIX Collaboration at RHIC shows that standard in-medium effects of the ρ,ω vector mesons—compatible with the NA60 data for In+In at and the CERES data for Pb+Au at —do not explain the large enhancement observed in the invariant mass regime from 0.2 to 0.5 GeV in Au+Au collisions at relative to pp collisions.     

Non-Abelian duality from vortex moduli: A dual model of color-confinement

It is argued that the dual transformation of non-Abelian monopoles occurring in a system with gauge symmetry breaking G→H is to be defined by setting the low-energy H system in Higgs phase, so that the dual system is in confinement phase. The transformation law of the monopoles follows from that of monopole-vortex mixed configurations in the system (with a large hierarchy of energy scales, v₁v₂) , under an unbroken, exact color-flavor diagonal symmetry . The transformation property among the regular monopoles characterized by π₂(G/H), follows from that among the non-Abelian vortices with flux quantized according to π₁(H), via the isomorphism π₁(G)π₁(H)/π₂(G/H). Our idea is tested against the concrete models—softly-broken supersymmetric SU(N), SO(N) and USp(2N) theories, with appropriate number of flavors. The results obtained in the semiclassical regime (at v₁v₂Λ) of these models are consistent with those inferred from the fully quantum-mechanical low-energy effective action of the systems (at v₁,v₂Λ).     

Search for the rare decays , , and

Rare decay modes , J/ψ→D⁻π⁺+c.c., and are searched for using events collected with the BESII detector at the BEPC. No signal above background is observed. We present upper limits on the branching fractions of , B(J/ψ→D⁻π⁺)<7.5×10⁻⁵, and at the 90% confidence level.     

Optical–optical double resonance spectroscopy of the transition of CaOH

The state of CaOH was investigated using optical–optical double resonance spectroscopy. A combined least-squares fit of the double resonance transition data along with optical transition data and the millimeter-wave pure rotational data of the state was performed using an effective Hamiltonian. The spin–rotation constant was determined for the state for the first time. An analysis of these constants showed that the Ca–O bond length and spin–rotation parameter of the state have the smallest values of all the observed ²Σ⁺ states of CaOH. This evidence suggests the assignment of the state as arising from a Ca⁺ atomic orbital of mainly 5sσ character. This atomic orbital assignment was shown to be consistent with both previous work on CaF and recent theoretical calculations on CaOH.     

Scaling and long-range dependence in option pricing I: Pricing European option with transaction costs under the fractional Black–Scholes model

This paper deals with the problem of discrete time option pricing by the fractional Black–Scholes model with transaction costs. By a mean self-financing delta-hedging argument in a discrete time setting, a European call option pricing formula is obtained. The minimal price of an option under transaction costs is obtained as timestep , which can be used as the actual price of an option. In fact, is an adjustment to the volatility in the Black–Scholes formula by using the modified volatility to replace the volatility σ, where is the Hurst exponent, and k is a proportional transaction cost parameter. In addition, we also show that timestep and long-range dependence have a significant impact on option pricing.     

Type I quasi-phase-matched blue second harmonic generation with different polarizations in periodically poled LiNbO3

First-order type I quasi-phase-matched (QPM) blue second-harmonic generation was demonstrated in periodically poled LiNbO₃ with period of 14.5 μm using d₃₁. 52 μJ of harmonic blue light at 0.473 μm was generated pumped by 114 μJ 35 ps pulse laser at 0.946 μm at 150 °C with a conversion efficiency of 45.6%. The average conversion efficiencies of 41.3% and 19% were also obtained at 150 °C, respectively, in the conventional first- and third-order QPM blue second-harmonic generation at 0.473 μm. The temperature acceptance bandwidths of 20 mm length periodically poled LiNbO₃ with first-order grating periods of 14.5 and 4.5 μm are 2.0 and 0.9 °C, respectively. The larger acceptance bandwidths and grating period for than those for enhance the frequency conversion efficiency, which shows the polarization dependence of quasi-phase matching.     

Fractional quasiexcitons in incompressible electron liquids

A new kind of many-body excitonic state composed of fractionally charged constituents is introduced. The constituents are a trion (X^-) embedded in an incompressible electron liquid and Laughlin quasiholes (QH's). Laughlin electron–trion correlations lead to an effective trion charge of -e/3. This many-body excitation is called “quasiexciton” and denoted by to distinguish it from a normal trion. The can bind one or two (e/3)-charged QH's, giving a neutral or a positive . The energy spectra and photoluminescence from radiative quasiexciton decay are studied numerically and interpreted using a generalized composite Fermion model of the e–X^- fluid.     

Structural and electronic behavior of Sr2GdRuO6 complex perovskite

We report experimental and theoretical study of crystallographic lattice and electronic structure of Sr₂GdRuO₆ complex perovskite, which is used as precursor in the fabrication process of superconducting ruthenocuprate RuSr₂GdCu₂O₈. Samples were produced by the standard solid state reaction. Rietveld refinement of experimental X-ray diffraction patterns shows that material crystallizes in a monoclinic structure, which belongs to the P2₁/n (#14) space group, with lattice parameters , , , and tilt angle β=90.258. Calculations of electronic structure were performed by the density functional theory. The exchange and correlation potentials were included through the LDA+U approximation. Density of states (DOS) study was carried out considering the two spin polarizations. Results show Gd are majority responsible for the magnetic character in this material, but Ru contribution is also relevant because d-orbital is closer to Fermi level. Theoretical results evidence that Sr₂GdRuO₆ material behaves as a magnetic semiconductor, with 20μ_B effective magnetic moment.     

Tunneling conductance in a gapped graphene-based superconducting structure: Case of massive Dirac electrons

The tunneling conductance in a NG/SG graphene junction in which the graphene was grown on a SiC substrate is simulated. The carriers in the normal graphene (NG) and the superconducting graphene (SG) are treated as massive relativistic particles. It is assumed that the Fermi energy in the NG and SG are E_FN400 meV and E_FS400 meV+U, respectively. Here U is the electrostatic potential from the superconducting gate electrode. It is seen that the Klein tunneling disappears in the case where a gap exist in the energy spectrum. As U→∞, the zero bias normalized conductance becomes persistent at a minimal value of G/G₀1.2. The normalized conductance G/G₀ is found to depend linearly on U with constant slope of , where is the size of the gap Δ opening up in the energy spectrum of the graphene grown on the SiC substrate. It is found that G/G₀2+αU for potentials in the range −270 meV<U<0 meV and G=0 for potentials U<−270 meV. As α→∞, the conductance for eV=Δ (V is the bias voltage placed across the NG/SG junction) can be approximated by a unit step function G(eV=Δ,U)/G₀2Θ(U). This last behavior indicates that a NG/SG junction made with gapped graphene could be used as a nano switch having excellent characteristics.     

Influence of spin on the activation energies at

The activation energy Δ of the fractional quantum Hall state at constant filling factor and also at and has been measured as a function of the perpendicular magnetic field B while modulating the electron density via a top gate. At small magnetic fields we observe a linear increase of Δ with the magnetic field. The slope of Δ vs. B allows us to directly extract the composite fermion g-factor.     

Spin susceptibility and effective mass of a 2D electron system in GaAs heterostructures towards the weak interacting regime

We determined the spin susceptibility χ and the effective mass m^* towards the high density limit. Using a tunable GaAs/AlGaAs heterostructure, we can vary the 2D electron density from to . From to our highest densities the mass values fall 10% below the band mass of GaAs. The enhancement of χ decreases monotonically from a factor of 3 to 0.88 with increasing density. It continues to follow a previously observed power law, which leads to an unphysical limit for n→∞. Band structure effects affecting mass and g-factor become appreciable for large n and, when taken into account, lead to the correct limiting behavior of χ. Numerical calculations are in qualitative agreement with our data but differ in detail.