Matrix elements and duality for type 2 unitary representations of the Lie superalgebra gl(m|n)

The characteristic identity formalism discussed in our recent articles is further utilized to derive matrix elements of type 2 unitary irreducible $gl(m|n)$ modules. In particular, we give matrix element formulae for all gl(m|n) generators, including the non-elementary generators, together with their phases on finite dimensional type 2 unitary irreducible representations. Remarkably, we find that the type 2 unitary matrix element equations coincide with the type 1 unitary matrix element equations for non-vanishing matrix elements up to a phase.Comment: 24 pages. arXiv admin note: text overlap with arXiv:1311.424

Reduced Wigner coefficients for Lie superalgebra gl(m|n) corresponding to unitary representations and beyond

In this paper fundamental Wigner coefficients are determined algebraically by considering the eigenvalues of certain generalized Casimir invariants. Here this method is applied in the context of both type 1 and type 2 unitary representations of the Lie superalgebra gl(mjn). Extensions to the non-unitary case are investigated. A symmetry relation between two classes of Wigner coefficients is given in terms of a ratio of dimensions.Comment: 17 page

Characteristic identities for Lie (super)algebras

We present an overview of characteristic identities for Lie algebras and superalgebras. We outline methods that employ these characteristic identities to deduce matrix elements of finite dimensional representations. To demonstrate the theory, we look at the examples of the general linear Lie algebras and Lie superalgebras.Comment: 10 pages, contribution to the 30th International Colloquium on Group Theoretical Methods in Physics (Group30) in Ghent, Belgium. Journal of Physics: Conference Series (to appear

Landau-Zener Problem for Trilinear Hamiltonians

We consider a nonlinear version of the Landau-Zener problem, focusing on photoassociation of a Bose-Einstein condensate as a specific example. Contrary to the exponential rate dependence obtained for the linear problem, a series expansion technique indicates that, when the resonance is crossed slowly, the probability for failure of adiabaticity is directly proportional to the rate at which the resonance is crossed.Comment: 4.5 pages, 1 figure, transferred to PRA; v2 adds discussion, clarification, and explicit numbers for Na and 87R

KELT-3b: A Hot Jupiter Transiting a V=9.8 Late-F Star

We report the discovery of KELT-3b, a moderately inflated transiting hot Jupiter with a mass of 1.477 (-0.067, +0.066) M_J, and radius of 1.345 +/- 0.072 R_J, with an orbital period of 2.7033904 +/- 0.000010 days. The host star, KELT-3, is a V=9.8 late F star with M_* = 1.278 (-0.061, +0.063) M_sun, R_* = 1.472 (-0.067, +0.065) R_sun, T_eff = 6306 (-49, +50) K, log(g) = 4.209 (-0.031, +0.033), and [Fe/H] = 0.044 (-0.082, +0.080), and has a likely proper motion companion. KELT-3b is the third transiting exoplanet discovered by the KELT survey, and is orbiting one of the 20 brightest known transiting planet host stars, making it a promising candidate for detailed characterization studies. Although we infer that KELT-3 is significantly evolved, a preliminary analysis of the stellar and orbital evolution of the system suggests that the planet has likely always received a level of incident flux above the empirically-identified threshold for radius inflation suggested by Demory & Seager (2011).Comment: 12 pages, 12 figures, accepted to Ap

KELT-6b: A P~7.9 d Hot Saturn Transiting a Metal-Poor Star with a Long-Period Companion

We report the discovery of KELT-6b, a mildly-inflated Saturn-mass planet transiting a metal-poor host. The initial transit signal was identified in KELT-North survey data, and the planetary nature of the occulter was established using a combination of follow-up photometry, high-resolution imaging, high-resolution spectroscopy, and precise radial velocity measurements. The fiducial model from a global analysis including constraints from isochrones indicates that the V=10.38 host star (BD+31 2447) is a mildly evolved, late-F star with T_eff=6102 \pm 43 K, log(g_*)=4.07_{-0.07}^{+0.04} and [Fe/H]=-0.28 \pm 0.04, with an inferred mass M_*=1.09 \pm 0.04 M_sun and radius R_star=1.58_{-0.09}^{+0.16} R_sun. The planetary companion has mass M_P=0.43 \pm 0.05 M_J, radius R_P=1.19_{-0.08}^{+0.13} R_J, surface gravity log(g_P)=2.86_{-0.08}^{+0.06}, and density rho_P=0.31_{-0.08}^{+0.07} g~cm^{-3}. The planet is on an orbit with semimajor axis a=0.079 \pm 0.001 AU and eccentricity e=0.22_{-0.10}^{+0.12}, which is roughly consistent with circular, and has ephemeris of T_c(BJD_TDB)=2456347.79679 \pm 0.00036 and P=7.845631 \pm 0.000046 d. Equally plausible fits that employ empirical constraints on the host star parameters rather than isochrones yield a larger planet mass and radius by ~4-7%. KELT-6b has surface gravity and incident flux similar to HD209458b, but orbits a host that is more metal poor than HD209458 by ~0.3 dex. Thus, the KELT-6 system offers an opportunity to perform a comparative measurement of two similar planets in similar environments around stars of very different metallicities. The precise radial velocity data also reveal an acceleration indicative of a longer-period third body in the system, although the companion is not detected in Keck adaptive optics images.Comment: Published in AJ, 17 pages, 15 figures, 6 table

Matrix elements for type 1 unitary irreducible representations of the Lie superalgebra gl(m|n)

Using our recent results on eigenvalues of invariants associated to the Lie superalgebra gl(m|n), we use characteristic identities to derive explicit matrix element formulae for all gl(m|n) generators, particularly non-elementary generators, on finite dimensional type 1 unitary irreducible representations.We compare our results with existingworks that deal with only subsets of the class of type 1 unitary representations, all of which only present explicit matrix elements for elementary generators. Our work therefore provides an important extension to existing methods, and thus highlights the strength of our techniques which exploit the characteristic identities