112 research outputs found
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
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
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