Improved measurement of the hydrogen 1S-2S transition frequency

We have measured the 1S-2S transition frequency in atomic hydrogen via two-photon spectroscopy on a 5.8 K atomic beam. We obtain f(1S-2S) = 2,466,061,413,187,035 (10) Hz for the hyperfine centroid, in agreement with, but 3.3 times better than the previous result [M. Fischer et al., Phys. Rev. Lett. 92, 230802 (2004)]. The improvement to a fractional frequency uncertainty of 4.2 × 10(-15) arises mainly from an improved stability of the spectroscopy laser, and a better determination of the main systematic uncertainties, namely, the second order Doppler and ac and dc Stark shifts. The probe laser frequency was phase coherently linked to the mobile cesium fountain clock FOM via a frequency comb.     

Lossless strip-to-slot waveguide transformer

We present a highly efficient integratable waveguide transformer that is capable of converting Gaussian-like waveguide modes to much more complicated non-Gaussian-like slot-waveguide modes, and vice versa. The structure consists of several pairs of complementary tapers capable of making this mode conversion virtually lossless. The capability of extremely low-loss mode transformation between these two classes of waveguides has been demonstrated by means of single- and double-slot transformers. Our simulation has shown that the total transformation losses are less than 0.01 and 0.02 dB per transformer, respectively, and can be easily achieved, with a total device length of less than 100 microm.     

Spectroscopic study of BixEu1−xVO4 and BiyGd1−yVO4 mixed oxides

The mixed oxides Bi_xEu_1−xVO₄ and Bi_yGd_1−yVO₄ crystallize in a zircon-type structure, for 0 <x < 0.6 and 0 < y < 0.64, and in a fergusonite-type structure, for 0.94 < x < 1 and 0.93 < y < 1. A process of competition between the dominant and the constrained effects of the lone-pair 6s² of Bi³⁺ is discussed. The diffuse reflectance spectroscopic studies of these mixed oxides are presented. The observed broad bands are attributed to charge transfer processes and the sharp peaks in the Bi_xEu_1−xVO₄ spectra are ascribed to intra-configurational 4f – 4ftransitions of the Eu³⁺ ion. The broad absorption shift in BiLnVO₄ (Ln : Eu and Gd) compounds to the longer wavelengths range, when Bi is introduced in the LnVO₄ lattice, is ascribed to charge transfer processes in a Bi-VO₄ center and are interpreted assuming a Jahn-Teller effect in the excited state of Bi³⁺. The concept of an internal pressure of Bi³⁺ ions is also used to explain the broad A-band shifts.     

On Certain Perturbations of the Erdös–Renyi Random Graph

We study perturbations of the Erdös–Renyi model for which the statistical weight of a graph depends on the abundance of certain geometrical patterns. Using the formal correspondance with an exactly solvable effective model, we show the existence of a percolation transition in the thermodynamical limit and derive perturbatively the expression of the threshold. The free energy and the moments of the degree distribution are also computed perturbatively in that limit and the percolation criterion is compared with the Molloy–Reed criterion.     

Towards the synthesis of MAX-phase functional coatings by pulsed laser deposition

Pulsed laser deposition with a Nd:YAG laser was used to grow thin films from a pre-synthesized Ti₃SiC₂ MAX-phase formulated ablation target on oxidized Si(1 0 0) and MgO(1 0 0) substrates. The depositions were carried out in a substrate temperature range from 300 to 900 K, and the pressure in the deposition chamber ranged from vacuum (10⁻⁵ Pa) to 0.05 Pa Argon background pressure. The properties of the films have been investigated by Rutherford backscattering spectrometry for film thickness and stoichiometric composition and X-ray diffraction for the crystallinity of the films. The silicon content of the films varied with the energy density of the laser beam. To suppress especially the silicon re-sputtering from the substrate, the energy of the incoming particles must be below a threshold of 20 eV. Therefore, the energy density of the laser beam must not be too high. At constant deposition energy density the film thickness depends strongly on the background pressure. The X-ray diffraction measurements show patterns that are typical of amorphous films, i.e. no Ti₃SiC₂ related reflections were found. Only a very weak TiC(2 0 0) reflection was seen, indicating the presence of a small amount of crystalline TiC.     

Sound propagation above a porous road surface with extended reaction by boundary element method

Acoustic impedance of an absorbing interface is easily introduced in boundary element codes provided that a local reaction is assumed. But this assumption is not valid in the case of porous road surface. A two-domain approach was developed for the prediction of sound propagation above a porous layer that takes into account the sound propagation inside the porous material. The porous material is modeled by a homogeneous dissipative fluid medium. An alternative to this time consuming two-domain approach is proposed by using the grazing incidence approximate impedance in the traditional single-domain boundary element method (BEM). It can be checked that this value is numerically consistent with the surface impedance calculated at the interface from the pressure and surface velocity solutions of the two-domain approach. The single-domain BEM introducing this grazing incidence impedance is compared in terms of sound attenuation with analytical solutions and two-domain BEM. The comparison is also performed with the single-domain BEM using the normal incidence impedance, and reveals a much better accuracy for the prediction of sound propagation above a porous interface.     

Anti de Sitter Quantum Field Theory and a New Class of Hypergeometric Identities

We use Anti-de Sitter quantum field theory to prove a new class of identities between hypergeometric functions related to the Källén-Lehmann representation of products of two Anti-de Sitter two-point functions. A rich mathematical structure emerges. We apply our results to study the decay of unstable Anti-de Sitter particles. The total amplitude is in this case finite and Anti-de Sitter invariant.     

Antiferromagnetic ordering in REM cobaltite GdCoO<Subscript>3</Subscript>

Temperature and magnetic-field dependences of the static magnetization of polycrystalline cobaltite GdCoO₃ have been measured. The magnetic properties of the GdCoO₃ sample have been studied in the paramagnetic and antiferromagnetic states. The magnetic phase diagram has been constructed. The exchange field between the Gd-Gd sublattices and the anisotropy field have been estimated.