Closed-Form Approximation for Parallel-Plate Waveguide Coefficients

Simple closed-form formulas for calculating coefficients of modes excited in a parallel-plate waveguide illuminated by a planar wave are presented. The mode-matching technique and Green’s formula are used to arrive at a matrix-based expression for waveguide coefficients calculation. Simplified solution to this matrix is proposed to derive approximate mode coefficient formulas in closed-form for both TE and TM polarization. The results are validated by numerical simulations and show good accuracy for all incidence angles and in broad frequency range

Integral formulas for wave functions of quantum many-body problems and representations of gl(n)

We derive explicit integral formulas for eigenfunctions of quantum integrals of the Calogero-Sutherland-Moser operator with trigonometric interaction potential. In particular, we derive explicit formulas for Jack's symmetric functions. To obtain such formulas, we use the representation of these eigenfunctions by means of traces of intertwining operators between certain modules over the Lie algebra $\frak gl_n$, and the realization of these modules on functions of many variables.Comment: 6 pages. One reference ([FF]) has been corrected. New references and an introduction have been adde

Charged particle in higher dimensional weakly charged rotating black hole spacetime

We study charged particle motion in weakly charged higher dimensional black holes. To describe the electromagnetic field we use a test field approximation and use the higher dimensional Kerr-NUT-(A)dS metric as a background geometry. It is shown that for a special configuration of the electromagnetic field the equations of motion of charged particles are completely integrable. The vector potential of such a field is proportional to one of the Killing vectors (called primary Killing vector) from the `Killing tower' of symmetry generating objects which exists in the background geometry. A free constant in the definition of the adopted electromagnetic potential is proportional to the electric charge of the higher dimensional black hole. The full set of independent conserved quantities in involution is found. It is demonstrated, that Hamilton-Jacobi equations are separable, as well as the corresponding Klein-Gordon equation and its symmetry operators.Comment: 9 pages, no figure

A novel strong coupling expansion of the QCD Hamiltonian

Introducing an infinite spatial lattice with box length a, a systematic expansion of the physical QCD Hamiltonian in \lambda = g^{-2/3} can be obtained. The free part is the sum of the Hamiltonians of the quantum mechanics of spatially constant fields for each box, and the interaction terms proportional to \lambda^n contain n discretised spatial derivatives connecting different boxes. As an example, the energy of the vacuum and the lowest scalar glueball is calculated up to order \lambda^2 for the case of SU(2) Yang-Mills theory.Comment: Talk given at the 6th International Workshop on "Critical Point and Onset of Deconfinement (CPOD)", Dubna, Russia, 23-29 August 201

A Lack of Resolved Near-Infrared Polarization Across the Face of M51

The galaxy M51 was observed using the Mimir instrument on the Perkins telescope to constrain the resolved H-band (1.6 $\mu$m) polarization across the galaxy. These observations place an upper limit of $P_H<0.05$ on the $H$-band polarization across the face of M51, at 0.6 arcsecond pixel sampling. Even with smoothing to coarser angular resolutions, to reduce polarization uncertainty, the $H$-band polarization remains undetected. The polarization upper limit at $H$-band, when combined with previous resolved optical polarimetry, rules out a Serkowski-like polarization dependence on wavelength. Other polarization mechanisms cannot account for the observed polarization ratio ($P_H/P{VRI} \lesssim 0.05$) across the face of M51.Comment: 4 pages, 2 figures, Accepted for publication in ApJ

H II Region Driven Galactic Bubbles And Their Relationship To The Galactic Magnetic Field

The relative alignments of mid-infrared traced Galactic bubbles are compared to the orientation of the mean Galactic magnetic field in the disk. The orientations of bubbles in the northern Galactic plane were measured and are consistent with random orientations-no preferential alignment with respect to the Galactic disk was found. A subsample of H II region driven Galactic bubbles was identified, and as a single population they show random orientations. When this subsample was further divided into subthermal and suprathermal H II regions, based on hydrogen radio recombination linewidths, the subthermal H II regions showed a marginal deviation from random orientations, but the suprathermal H II regions showed significant alignment with the Galactic plane. The mean orientation of the Galactic disk magnetic field was characterized using new near-infrared starlight polarimetry and the suprathermal H II regions were found to preferentially align with the disk magnetic field. If suprathermal linewidths are associated with younger H II regions, then the evolution of young H II regions is significantly affected by the Galactic magnetic field. As H II regions age, they cease to be strongly linked to the Galactic magnetic field, as surrounding density variations come to dominate their morphological evolution. From the new observations, the ratios of magnetic-to-ram pressures in the expanding ionization fronts were estimated for younger H II regions.NSF AST 06-07500, 09-07790NASAW. M. Keck FoundationAstronom