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 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

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

Numerical test for hyperbolicity of chaotic dynamics in time-delay systems

We develop a numerical test of hyperbolicity of chaotic dynamics in time-delay systems. The test is based on the angle criterion and includes computation of angle distributions between expanding, contracting and neutral manifolds of trajectories on the attractor. Three examples are tested. For two of them previously predicted hyperbolicity is confirmed. The third one provides an example of a time-delay system with nonhyperbolic chaos.Comment: 7 pages, 5 figure

New Metrics Admitting the Principal Killing-Yano Tensor

It is believed that in any number of dimensions the off-shell Kerr-NUT-(A)dS metric represents a unique geometry admitting the principal (rank 2, non-degenerate, closed conformal Killing-Yano) tensor. The original proof relied on the Euclidean signature and therein natural assumption that the eigenvalues of the principal tensor have gradients of spacelike character. In this paper we evade this common wisdom and construct new classes of Lorentzian (and other signature) off-shell metrics admitting the principal tensor with null eigenvalues, uncovering so a much richer structure of spacetimes with principal tensor in four and higher dimensions. A few observations regarding the Kerr-Schild ansatz are also made.Comment: 9 pages, no figures. v2: minor expansions, added reference

Quantum Computing, Metrology, and Imaging

Information science is entering into a new era in which certain subtleties of quantum mechanics enables large enhancements in computational efficiency and communication security. Naturally, precise control of quantum systems required for the implementation of quantum information processing protocols implies potential breakthoughs in other sciences and technologies. We discuss recent developments in quantum control in optical systems and their applications in metrology and imaging.Comment: 11 pages, 6 figures; Proceedings of SPIE: Fluctuations and Noise in Photonics and Quantum Optics III (2005

Weakly charged generalized Kerr-NUT-(A)dS spacetimes

We find an explicit solution of the source free Maxwell equations in a generalized Kerr-NUT-(A)dS spacetime in all dimensions. This solution is obtained as a linear combination of the closed conformal Killing-Yano tensor $h_{ab}$, which is present in such a spacetime, and a derivative of the primary Killing vector, associated with $h_{ab}$. For the vanishing cosmological constant the obtained solution reduces to the Wald's electromagnetic field generated from the primary Killing vector.Comment: 4 pages, no figures v2: added reference