Explicit computation of shear three-point correlation functions: the one-halo model case

We present a method for calculating explicit expressions of the shear three-point function for various cosmological models. The method is applied here to the one-halo model in case of power law density profiles for which results are detailed. The three-point functions are found to reproduce to a large extent patterns in the shear correlations obtained in numerical simulations and may serve as a guideline to implement optimized methods for detecting the shear three-point function. In principle, the general method presented here can also be applied for other models of matter correlation.Comment: 8 pages, 6 figures, submitted to A

The infrared conductivity of Nax_xCoO2_2: evidence of gapped states

We present infrared ab-plane conductivity data for the layered cobaltate Na$_x$CoO$_2$ at three different doping levels ($x=0.25, 0.50$, and 0.75). The Drude weight increases monotonically with hole doping, $1-x$. At the lowest hole doping level $x$=0.75 the system resembles the normal state of underdoped cuprate superconductors with a scattering rate that varies linearly with frequency and temperature and there is an onset of scattering by a bosonic mode at 600 \cm. Two higher hole doped samples ($x=0.50$ and 0.25) show two different-size gaps (110 \cm and 200 \cm, respectively) in the optical conductivities at low temperatures and become insulators. The spectral weights lost in the gap region of 0.50 and 0.25 samples are shifted to prominent peaks at 200 \cm and 800 \cm, respectively. We propose that the two gapped states of the two higher hole doped samples ($x$=0.50 and 0.25) are pinned charge ordered states.Comment: 4 pages, 3 figure

Correlation between Tc and Lattice Parameters of Novel Superconducting NaxCoO2 yH2O

We synthesized the five batches of the samples of the novel P3 type superconductor, Na$_{x}$(H$_{3}$O)$_{y'}$CoO$_{2}\cdot y''$H$_{2}$O, by the soft chemical process starting from $\alpha$-NaCoO$_{2}$. The chemical and structural properties varied rather widely from batch to batch, with a result that $T_{c}$ varied from 4.6 K to 3.2 K. The magnetic susceptibility above $T_{c}$ shows upturn at low temperature as in the case of the P2 phase. The $T_{c}$ seems to be well correlated to the lattice parameters.Comment: 2 pages, 2 figures, and 1 table, to be published in J. Phys. Soc. Jpn. 73 (9) with possible minor revision

Implication of Omega_m through the Morphological Analysis of Weak Lensing Fields

We apply the morphological descriptions of two-dimensional contour map, the so-called Minkowski functionals (the area fraction, circumference, and Euler characteristics), to the convergence field $\kappa(\bm{\theta})$ of the large-scale structure reconstructed from the shear map produced by the ray-tracing simulations. The perturbation theory of structure formation has suggested that the non-Gaussian features on the Minkowski functionals with respect to the threshold in the weakly nonlinear regime are induced by the three skewness parameters of $\kappa$ that are sensitive to the density parameter of matter, $\Omega_{\rm m}$. We show that, in the absence of noise due to the intrinsic ellipticities of source galaxies with which the perturbation theory results can be recovered, the accuracy of $\Omega_{\rm m}$ determination is improved by $\sim 20$ using the Minkowski functionals compared to the conventional method of using the direct measure of skewness.Comment: 4 pages, 3 figures, to appear in ApJ Lette

Behavior of a frustrated quantum spin chain with bond dimerization

We clarified behavior of the excitation gap in a frustrated S=1/2 quantum spin chain with bond dimerization by using the numerical diagonalization of finite systems and a variational approach. The model interpolates between the independent dimer model and the S=1 spin chain by changing a strength of the dimerization. The energy gap is minimum at the fully-frustrated point, where a localized kink and a freely mobile anti-kink govern the low-lying excitations. Away from the point, a kink and an antikink form a bound state by an effective triangular potential between them. The consequential gap enhancement and the localization length of the bound state is obtained exactly in the continuous limit. The gap enhancement obeys a power law with exponent 2/3. The method and the obtained results are common to other frustrated double spin-chain systems, such as the one-dimensional J_1 - J_2 model, or the frustrated ladder model.Comment: 11 pages, REVTeX, 8 figures in eps-fil

59Co-NMR Knight Shift of Superconducting Three-Layer NaxCoO2.yH2O

The superconducting state of NaxCoO2.yH2O with three CoO2 layers in a unit cell has been studied by 59Co-NMR. The Knight shift measured for a peak of the NMR spectra corresponding to the external magnetic field H along one of the principal directions within the CoO2 plane, exhibits a rapid decrease with decreasing temperature T below the superconducting transition temperature Tc, indicating that the spin susceptibility is suppressed in the superconducting phase, at least, for this field direction. Because differences of the superconducting properties are rather small between this three-layer NaxCoO2.yH2O and previously reported NaxCoO2.yH2O with two CoO2 layers within a unit cell, the present result of the Knight shift studies indicates that the Cooper pairs of the former system are in the singlet state as in the latter, for which the spin susceptibility is suppressed for both directions of H parallel and perpendicular to the CoO2 plane.Comment: 5 page

Electronic Collective Modes and Superconductivity in Layered Conductors

A distinctive feature of layered conductors is the presence of low-energy electronic collective modes of the conduction electrons. This affects the dynamic screening properties of the Coulomb interaction in a layered material. We study the consequences of the existence of these collective modes for superconductivity. General equations for the superconducting order parameter are derived within the strong-coupling phonon-plasmon scheme that account for the screened Coulomb interaction. Specifically, we calculate the superconducting critical temperature Tc taking into account the full temperature, frequency and wave-vector dependence of the dielectric function. We show that low-energy plasmons may contribute constructively to superconductivity. Three classes of layered superconductors are discussed within our model: metal-intercalated halide nitrides, layered organic materials and high-Tc oxides. In particular, we demonstrate that the plasmon contribution (electronic mechanism) is dominant in the first class of layered materials. The theory shows that the description of so-called ``quasi-two-dimensional superconductors'' cannot be reduced to a purely 2D model, as commonly assumed. While the transport properties are strongly anisotropic, it remains essential to take into account the screened interlayer Coulomb interaction to describe the superconducting state of layered materials.Comment: Final version (minor changes) 14 pages, 6 figure

Towards first-principles understanding of the metal-insulator transition in fluid alkali metals

By treating the electron-ion interaction as perturbation in the first-principles Hamiltonian, we have calculated the density response functions of a fluid alkali metal to find an interesting charge instability due to anomalous electronic density fluctuations occurring at some finite wave vector {\bi Q} in a dilute fluid phase above the liquid-gas critical point. Since |{\bi Q}| is smaller than the diameter of the Fermi surface, this instability necessarily impedes the electric conduction, implying its close relevance to the metal-insulator transition in fluid alkali metals.Comment: 11 pages, 5 figure

Three-Point Correlations in Weak Lensing Surveys: Model Predictions and Applications

We use the halo model of clustering to compute two- and three-point correlation functions for weak lensing, and apply them in a new statistical technique to measure properties of massive halos. We present analytical results on the eight shear three-point correlation functions constructed using combination of the two shear components at each vertex of a triangle. We compare the amplitude and configuration dependence of the functions with ray-tracing simulations and find excellent agreement for different scales and models. These results are promising, since shear statistics are easier to measure than the convergence. In addition, the symmetry properties of the shear three-point functions provide a new and precise way of disentangling the lensing E-mode from the B-mode due to possible systematic errors. We develop an approach based on correlation functions to measure the properties of galaxy-group and cluster halos from lensing surveys. Shear correlations on small scales arise from the lensing matter within halos of mass M > 10^13 solar masses. Thus the measurement of two- and three-point correlations can be used to extract information on halo density profiles, primarily the inner slope and halo concentration. We demonstrate the feasibility of such an analysis for forthcoming surveys. We include covariances in the correlation functions due to sample variance and intrinsic ellipticity noise to show that 10% accuracy on profile parameters is achievable with surveys like the CFHT Legacy survey, and significantly better with future surveys. Our statistical approach is complementary to the standard approach of identifying individual objects in survey data and measuring their properties.Comment: 30 pages, 21 figures. Corrected typos in equations (23) and (28). Matches version for publication in MNRA