Generalized MICZ-Kepler Problems and Unitary Highest Weight Modules

For each integer $n\ge 1$, we demonstrate that a $(2n+1)$-dimensional generalized MICZ-Kepler problem has an \mr{Spin}(2, 2n+2) dynamical symmetry which extends the manifest \mr{Spin}(2n+1) symmetry. The Hilbert space of bound states is shown to form a unitary highest weight \mr{Spin}(2, 2n+2)-module which occurs at the first reduction point in the Enright-Howe-Wallach classification diagram for the unitary highest weight modules. As a byproduct, we get a simple geometric realization for such a unitary highest weight \mr{Spin}(2, 2n+2)-module.Comment: 27 pages, Refs. update

qq-Trinomial identities

We obtain connection coefficients between $q$-binomial and $q$-trinomial coefficients. Using these, one can transform $q$-binomial identities into a $q$-trinomial identities and back again. To demonstrate the usefulness of this procedure we rederive some known trinomial identities related to partition theory and prove many of the conjectures of Berkovich, McCoy and Pearce, which have recently arisen in their study of the $\phi_{2,1}$ and $\phi_{1,5}$ perturbations of minimal conformal field theory.Comment: 21 pages, AMSLate

Quantum communication and state transfer in spin chains

We investigate the time evolution of a single spin excitation state in certain linear spin chains, as a model for quantum communication. We consider first the simplest possible spin chain, where the spin chain data (the nearest neighbour interaction strengths and the magnetic field strengths) are constant throughout the chain. The time evolution of a single spin state is determined, and this time evolution is illustrated by means of an animation. Some years ago it was discovered that when the spin chain data are of a special form so-called perfect state transfer takes place. These special spin chain data can be linked to the Jacobi matrix entries of Krawtchouk polynomials or dual Hahn polynomials. We discuss here the case related to Krawtchouk polynomials, and illustrate the possibility of perfect state transfer by an animation showing the time evolution of the spin chain from an initial single spin state. Very recently, these ideas were extended to discrete orthogonal polynomials of q-hypergeometric type. Here, a remarkable result is a new analytic model where perfect state transfer is achieved: this is when the spin chain data are related to the Jacobi matrix of q-Krawtchouk polynomials. This case is discussed here, and again illustrated by means of an animation

RR Lyrae Variables in the Globular Cluster M55. The First Evidence for Non Radial Pulsations in RR Lyr Stars

We present the results of a photometric study of RR Lyrae variables in the field of the globular cluster M55. We have discovered nine new RR Lyrae stars, increasing the number of known variables in this cluster to 15 objects. Five of the newly discovered variables belong to Bailey type RRc and two to type RRab. Two background RRab stars are probable members of the Sagittarius dwarf galaxy. Fourier decomposition of the light curves was used to derive basic properties of the present sample of RR Lyrae variables. From an analysis of the RRc variables we obtain a mean mass of $M=0.53\pm0.03 M_\odot$, luminosity $\log L=1.75\pm0.01$, effective temperature $T_{eff}=7193\pm27$ K, and helium abundance $Y=0.27\pm0.01$. Based on the $B-V$ colors, periods and metallicities of the RRab stars we estimate the value of the color excess for M55 to be equal to $E(B-V)=0.11\pm0.03$. Using this value we derive the colors of the blue and red edges of the instability strip in M55. The blue edge lies at $(B-V)_0=0.20$ mag and the red edge lies at $(B-V)_0=0.38$ mag. We estimate the values of the visual apparent and dereddened distance moduli to be $13.65\pm0.11$ and $13.31\pm0.11$, respectively. The light curves of three of the RRc variables exhibit changes in amplitude of over 0.1 mag on the time scale of less than a week, rather short for the Blazhko effect, but with no evidence for another radial pulsational frequency. However we do detect other periodicities which are clearly visible in the light curve after removing variations with the first overtone radial frequency. This is strong evidence for the presence of non-radial pulsations, a behavior common for $\delta$ Scuti stars but not yet observed among RR Lyr variables.Comment: submitted to Astronomical Journal, 33 pages with 11 figure

Damage profiles of ultrashallow B implants in Si and the Kinchin-Pease relationship

Damage distributions resulting from 0.1-2 keV B+ implantation at room temperature into Si(100) to doses ranging from 1×1014 to 2×1016 cm-2 have been determined using high-depth-resolution medium-energy-ion scattering in the double alignment mode. For all B+ doses and energies investigated a 3-4 nm deep, near-surface damage peak was observed while for energies at and above 1 keV, a second damage peak developed beyond the mean projected B+ ion range of 5.3 nm. This dual damage peak structure is due to dynamic annealing processes. For the near-surface peak it is observed that, at the lowest implant energies and doses used, for which recombination processes are suppressed due to the proximity of the surface capturing interstitials, the value of the damage production yield for low-mass B+ ions is equal or greater than the modified Kinchin-Pease model predictions [G. H. Kinchin and R. S. Pease, Rep. Prog. Phys. 18, 1 (1955); G. H. Kinchin and R. S. Pease, J. Nucl. Energy 1, 200 (1955); P. Sigmund, Appl. Phys. Lett. 14, 114 (1969)]

Observing Strategies for the Detection of Jupiter Analogs

To understand the frequency, and thus the formation and evolution, of planetary systems like our own solar system, it is critical to detect Jupiter-like planets in Jupiter-like orbits. For long-term radial-velocity monitoring, it is useful to estimate the observational effort required to reliably detect such objects, particularly in light of severe competition for limited telescope time. We perform detailed simulations of observational campaigns, maximizing the realism of the sampling of a set of simulated observations. We then compute the detection limits for each campaign to quantify the effect of increasing the number of observational epochs and varying their time coverage. We show that once there is sufficient time baseline to detect a given orbital period, it becomes less effective to add further time coverage-rather, the detectability of a planet scales roughly as the square root of the number of observations, independently of the number of orbital cycles included in the data string. We also show that no noise floor is reached, with a continuing improvement in detectability at the maximum number of observations N = 500 tested here.Peer reviewe