On a problem of H. N. Gupta

It is shown that the axiom For any points x, y, z such that y is between x and z, there is a right triangle having x and z as endpoints of the hypotenuse and y as foot of the altitude to the hypotenuse, when added to three-dimensional Euclidean geometry over arbitrary ordered fields, is weaker than the axiom Every line which passes through the interior of a sphere intersects that sphere.     

Derivation of the probability distribution functions for succession quota random variables

The probability distribution functions (pdf's) of the sooner and later waiting time random variables (rv's) for the succession quota problem (k successes and r failures) are derived presently in the case of a binary sequence of order k. The probability generating functions (pgf's) of the above rv's are then obtained directly from their pdf's. In the case of independent Bernoulli trials, expressions for the pdf's in terms of binomial coefficients are also established.     

Electronic Raman scattering and phonon self-energy effects in the R-123 system: Signatures of gap and pseudogap

Using Raman spectroscopy and transport measurements we investigate thin epitaxial films of Y_1—x(Pr, Ca)_xBa₂Cu₃O_6+y. We explore the electronic Raman responses in A_1g, B_1g, and B_2g symmetry obtained after subtraction of phononic excitations, and especially, the 2Δ peaks that form out of the electronic background below T_c. We find that the energy of the B_1g 2Δ peak, which is a measure of the gap value, increases monotonically with decreasing doping until the peak becomes unresolvable. In contrast, the peak in A_1g symmetry follows T_c being still resolvable in the Pr-doped films. The B_2g response is weak and a 2Δ peak is only detected at the highest doping level. As a consequence of strong electron-phonon coupling, the B_1g phonon at ∼340 cm^—1 exhibits a pronounced Fano-type line shape. We use a phenomenological model to describe the line shape that takes into account real and imaginary part of the electronic response. It allows us to obtain the self-energy corrections and the mass-enhancement factor λ as a measure of the coupling. In the normal state we find λ = 0.015 around optimal doping and decreasing values with decreasing doping. The electron-phonon coupling increases strongly below T_c in overdoped samples in which the B_1g 2Δ peaks appear in the vicinity of the phonon. Self-energy effects observed in the superconducting state can only partly be assigned to the redistributing electronic response. Anomalies with respect to frequency, linewidth, and intensity remain. They appear at increasing temperatures with decreasing doping and we provide evidence that they are connected to the presence of the pseudogap. We supplement our study by a comparison with single crystal data and investigate the influence of site-substitutional disorder on the electronic response and the electron-phonon interaction.     

Phase transitions and positive definite couplings

The method of infrared bounds is extended to a large class of nearest neighbour interactions in classical spin systems. Temperature controlled bounds on fluctuations follow whenever the coupling function is a positive definite kernel. Existence of phase transitions is demonstrated for the RP ^Nmodel for d3.     

Unveiling the nature of three-dimensional orbital ordering transitions: the case of e(g) and t(2g) models on the cubic lattice

We perform large scale finite-temperature Monte Carlo simulations of the classical e(g) and t(2g) orbital models on the simple cubic lattice in three dimensions. The e(g) model displays a continuous phase transition to an orbitally ordered phase. While the correlation length exponent ν ≈ 0.66(1) is close to the 3D XY value, the exponent η ≈ 0.15(1) differs substantially from O(N) values. At T(c) a U(1) symmetry emerges, which persists for T < T(c) below a crossover length scaling as Λ ～ ξ(a), with an unusually small a ≈ 1.3. Finally, for the t(2g) model we find a first order transition into a low-temperature lattice-nematic phase without orbital order.     

Tailoring of high-Q-factor surface plasmon modes on silver microtubes

We investigate the excitation of surface plasmon polaritons on silver tubes with finite-difference time-domain simulations. These surface plasmon polaritons exhibit azimuthal whispering gallery modes with quality factors in the hundreds. We show that the high quality factors arise from the coupling of the surface plasmon modes to photonic modes inside the tube. We examine the influence of a gain material on the quality factors and find that for material data of rhodamine 6G, the quality factors are enhanced significantly up to values of 3000.     

Enhanced angular tolerance of resonant waveguide grating reflectors

We introduce an approach to enhance the angular tolerance of resonant waveguide gratings by stacking two resonant structures on top of each other. It is shown that reflectivities close to unity can be retrieved over the entire angular spectrum by a double T-shaped grating configuration. Although a combination of silicon as the high-index and diamond as the low-index material is considered, the principles of our new approach can also be used to realize monolithic silicon structures with similar properties. We illustrate that the functionality of the device can be understood by a decomposition into separated elements. Our approach might have compelling applications as new diffractive-reflective optical components with low-coating thermal noise in the field of high-precision metrology.     

Spectroscopy of the hyperfine structure of antiprotonic 4He and 3He

The spin magnetic moment $\mu^{\overline{p}}_{s}$ of the antiproton can be determined by comparing the measured transition frequencies in $\overline{p}^4$ He^?+? with three-body QED calculations. A comparison between the proton and antiproton can then be used as a test of CPT invariance. The highest measurement precision of the difference between the proton and the antiproton spin magnetic moments to date is 0.3%. A new experimental value of the spin magnetic moment of the antiproton was obtained as $\mu^{\overline{p}}_{s} = -2.7862(83)\mu_{N}$ , slightly better than the previously best measurement. This agrees with $\mu^{p}_{s}$ within 0.24%. In 2009, a new measurement with antiprotonic ³He has been started. A comparison between the theoretical calculations and experimental results would lead to a stronger test of the theory and address systematic errors therein. A measurement of this state will be the first HF measurement on $\overline{p}^3$ He^?+?. We report here on the new experimental setup and the first tests.