Spectra of Random Hermitian Matrices with a Small-Rank External Source: The Critical and Near-Critical Regimes

Random Hermitian matrices are used to model complex systems without time-reversal invariance. Adding an external source to the model can have the effect of shifting some of the matrix eigenvalues, which corresponds to shifting some of the energy levels of the physical system. We consider the case when the n×n external source matrix has two distinct real eigenvalues: a with multiplicity r and zero with multiplicity n−r. For a Gaussian potential, it was shown by Péché (Probab. Theory Relat. Fields 134:127–173, 2006) that when r is fixed or grows sufficiently slowly with n (a small-rank source), r eigenvalues are expected to exit the main bulk for |a| large enough. Furthermore, at the critical value of a when the outliers are at the edge of a band, the eigenvalues at the edge are described by the r-Airy kernel. We establish the universality of the r-Airy kernel for a general class of analytic potentials for r=O(n^g)r=\mathcal{O}(n^{\gamma}) for 0≤γ<1/12.     

Crystal growth,spectroscopic characterization and laser performance of Nd:Lu<Subscript>0.33</Subscript>Y<Subscript>0.36</Subscript>Gd<Subscript>0.3</Subscript>VO<Subscript>4</Subscript> crystal

A new three-matrix mixed vanadate crystal Nd:Lu_0.33Y_0.36Gd_0.3VO₄ (Nd:LuYGdVO₄) crystal was grown by the Czochralski method. Room temperature absorption and fluorescence spectra of the Nd:LuYGdVO₄ crystals were measured and the spectroscopic parameters were calculated by the Judd-Ofelt theory. The intensity parameters of the Nd:LuYGdVO₄ crystal were Ω₂ = 9.736 × 10⁻²⁰ cm², Ω₄ = 4.179 × 10⁻²⁰ cm², Ω₆ = 8.020 × 10⁻²⁰ cm² and the stimulate emission cross section was 5.3 × 10⁻¹⁹ cm². Diodepumped actively Q-switched and passively Q-switched Nd:LuYGdVO₄ and Nd:Lu_0.14Y_0.86VO₄ lasers at 1.06 μm were demonstrated. The results indicate that, for both actively and passively Q-switched lasers, the Nd:LuYGdVO₄ lasers can generate shorter pulse width with higher peak power than the Nd:Lu_0.14Y_0.86VO₄ lasers at the same cavity conditions.     

New Spectrofluorimetric Method for Determination of Cephalosporins in Pharmaceutical Formulations

Simple, accurate and sensitive spectrofluorimetric method has been proposed for the determination of three cephalosporins, namely; cefixime (cefi), cephalexine (ceph), cefotaxime sodium (cefo) in pharmaceutical formulations. The method is based on a reaction between cephalosporins with 1, 2-naphthoquinone-4-sulfonic (NQS) in alkaline medium, at pH values of 12.0 for cefi and 13.0 for ceph and cefo to give highly fluorescent derivatives extracted with chloroform and subsequently measured at 600,580 and 580 nm after excitation at 520,455 and 490 nm for cefi, ceph and cefo respectively. The optimum experimental conditions have been studied. Beer’s law is obeyed over the concentrations of 10–35 ng/mL, 10–60 ng/mL and 20–45 ng/mL for cefi,ceph and cefo, respectively. The detection limits were 2.02 ng/mL, 2.09 ng/mL and 2.30 ng/mL for cefi, ceph and cefo, respectively, with a linear regression correlation coefficient of 0.9987, 0.9995 and 0.9991 and recoveries in range from 98.5-107.04, 95.17-101.00 and 95.00-109.55% for cefi, ceph and cefo, respectively. This method is simple and can be applied for the determination of cefi, ceph and cefo in pharmaceutical formulations in quality control laboratories.     

Micro-wires self-assembled and 3D-connected with the help of a nematic liquid crystal

We discuss a method for producing automatic 3D connections at right places between substrates in front of one another. The idea is based on the materialization of disclination lines working as templates. The lines are first created in the nematic liquid crystal (5CB) at the very place where microwires have to be synthesized. Due to their anchoring properties, colloids dispersed into the nematic phase produce orientational distortions around them. These distortions, which may be considered as due to topological charges, result in a nematic force, able to attract the colloids towards the disclinations. Ultimately, the particles get trapped onto them, forming micro- or nano-necklaces. Before being introduced in the nematic phase, the colloids are covered with an adhering and conducting polypyrrole film directly synthesized at the surface of the particles (heterogeneous polymerization). In this manner, the particles become conductive so that we may finally perform an electropolymerization of pyrrole monomers solved in 5CB, and definitely stick the whole necklace. The electric connection thus synthesized is analyzed by AFM, and its strength is checked by means of hydrodynamic tests. This wiring method could allow Moore's law to overcome the limitations that arise when down-sizing the electronic circuits to nanometer scale.     

Conical spin-spiral state in an ultrathin film driven by higher-order spin interactions

We report a transverse conical spin spiral as the magnetic ground state of a double-layer Mn on a W(110) surface. Using spin-polarized scanning tunneling microscopy, we find a long-range modulation along the [001] direction with a periodicity of 2.4 nm coexisting with a local row-wise antiferromagnetic contrast. First-principles calculations reveal a transverse conical spin-spiral ground state of this system which explains the observed magnetic contrast. The canting of the spins is induced by higher-order exchange interactions, while the spiraling along the [001] direction is due to frustrated Heisenberg exchange and Dzyaloshinskii-Moriya interaction.     

The spin dynamics in distorted kagome lattices: a comparative Raman study

Despite the conceptional importance of realizing spin liquids in solid states only few compounds are known. On the other hand the effect of lattice distortions and anisotropies on the magnetic exchange topology and the fluctuation spectrum is an interesting problem. We compare the excitation spectra of the two s = 1/2 kagome lattice compounds, volborthite and vesignieite, using Raman scattering. We demonstrate that even small modifications of the crystal structure may have a huge effect on the phonon spectrum and low-temperature properties.     

Ultrafast quantum gates in circuit QED

We present a method to implement ultrafast two-qubit gates valid for the ultrastrong coupling and deep strong coupling regimes of light-matter interaction, considering state-of-the-art circuit quantum electrodynamics technology. Our proposal includes a suitable qubit architecture and is based on a four-step sequential displacement of the intracavity field, operating at a time proportional to the inverse of the resonator frequency. Through ab?initio calculations, we show that these quantum gates can be performed at subnanosecond time scales while keeping a fidelity above 99%.     

Wideband subwavelength gratings for coupling between silicon-on-insulator waveguides and optical fibers

We propose and experimentally demonstrate a novel subwavelength grating coupler on silicon-on-insulator, for coupling to optical fibers with a wide optical bandwidth. Theoretical analysis and design optimization of the coupler are described. About 73?nm 1?dB bandwidth was experimentally demonstrated with -5.6 dB coupling efficiency. Better than -3.4 dB efficiency with 86?nm 1?dB bandwidth is predicted for these structures with optimized buried oxide thickness.     

Comparative spectroscopic investigation of Yb3x Y3(1 ? x )Al5O12 (x = 3, 5, 10 and 15%) transparent ceramics

Transparent Yb_3x Y_{3(1 ? x} )Al₅O₁₂ (x = 3, 5, 10 and 15%) ceramics were fabricated by solid-state reaction and vacuum sintering method with a mixture of commercial Al₂O₃, Y₂O₃ and Yb₂O₃ powders. Ethanol and 0.5 wt % tetraethoxysilane were doped. Transparent fully dense samples with grain sizes of several micrometers were obtained by sintered at 1750 K. The absorption spectra, emission spectra and fluorescence life time of these transparent Yb_3x Y_{3(1 ? x} )Al₅O₁₂ ceramics at room temperature have been measured and calculated. The air annealed effects of Yb_3x Y_{3(1 ? x} )Al₅O₁₂ ceramics have been compared with un-annealed Yb:YAG transparent ceramics which shows the difference of the Yb³⁺ ions between annealed and unannealed Yb:YAG ceramics is less than 1%.     

Multichannel and omnidirectional transparency in periodic metamaterial layers

Multichannel and omnidirectional transmission can be realized in one-dimensional periodic metamaterial layers, where double-negative materials and single-negative materials are alternately stacked. The proposed structures can produce as many resonance transmission modes as desired by adjusting the number of the periods. Such transmission modes with perfect transmission are robust against incident angles and polarizations. The frequencies and frequency intervals of these modes can be tuned by changing the thicknesses of the metamaterial layers. Composite right/left-handed transmission lines with lumped elements (capacitors and inductors) were used to verify the characteristics of the considered system. Our findings provide an efficient way to select useful multiple channel signals from all directions, and it is useful in optoelectronic device applications.