13,999 research outputs found
An extension of SaalschĂźtz's summation theorem for the series <sub><i>r</i>+3</sub>F<sub><i>r</i>+2</sub>
The aim in this research note is to provide an extension of SaalschĂźtz's summation theorem for the series r+3Fr+2(1) when r pairs of numeratorial and denominatorial parameters differ by positive integers. The result is obtained by exploiting a generalization of an Euler-type transformation recently derived by Miller and Paris [Transformation formulas for the generalized hypergeometric function with integral parameter differences. Rocky Mountain J Math. 2013;43, to appear]
On a new class of summation formulae involving the Laguerre polynomial
By elementary manipulation of series, a general transformation involving the generalized hypergeometric function is established. Kummerâs first theorem, the classical Gauss summation theorem and the generalized Kummer summation theorem due to Lavoie et al. [Generalizations of Whippleâs theorem on the sum of a 3 F 2, J. Comput. Appl. Math. 72 (1996), pp. 293â300] are then applied to obtain a new class of summation formulae involving the Laguerre polynomial, which have not previously appeared in the literature. Several related results due to Exton have also been given in a corrected form
On two Thomae-type transformations for hypergeometric series with integral parameter differences
We obtain two new Thomae-type transformations for hypergeometric series with r pairs of numeratorial and denominatorial parameters differing by positive integers. This is achieved by application of the so-called Beta integral method developed by Krattenthaler and Rao [Symposium on Symmetries in Science (ed. B. Gruber), Kluwer (2004)] to two recently obtained Euler-type transformations. Some special cases are given
Superspace Formulation in a Three-Algebra Approach to D=3, N=4,5 Superconformal Chern-Simons Matter Theories
We present a superspace formulation of the D=3, N=4,5 superconformal
Chern-Simons Matter theories, with matter supermultiplets valued in a
symplectic 3-algebra. We first construct an N=1 superconformal action, and then
generalize a method used by Gaitto and Witten to enhance the supersymmetry from
N=1 to N=5. By decomposing the N=5 supermultiplets and the symplectic 3-algebra
properly and proposing a new super-potential term, we construct the N=4
superconformal Chern-Simons matter theories in terms of two sets of generators
of a (quaternion) symplectic 3-algebra. The N=4 theories can also be derived by
requiring that the supersymmetry transformations are closed on-shell. The
relationship between the 3-algebras, Lie superalgebras, Lie algebras and
embedding tensors (proposed in [E. A. Bergshoeff, O. Hohm, D. Roest, H.
Samtleben, and E. Sezgin, J. High Energy Phys. 09 (2008) 101.]) is also
clarified. The general N=4,5 superconformal Chern-Simons matter theories in
terms of ordinary Lie algebras can be rederived in our 3-algebra approach. All
known N=4,5 superconformal Chern-Simons matter theories can be recovered in the
present superspace formulation for super-Lie-algebra realization of symplectic
3-algebras.Comment: 37 pages, minor changes, published in PR
On Markovian solutions to Markov Chain BSDEs
We study (backward) stochastic differential equations with noise coming from
a finite state Markov chain. We show that, for the solutions of these equations
to be `Markovian', in the sense that they are deterministic functions of the
state of the underlying chain, the integrand must be of a specific form. This
allows us to connect these equations to coupled systems of ODEs, and hence to
give fast numerical methods for the evaluation of Markov-Chain BSDEs
Time-dependent Fr\"ohlich transformation approach for two-atom entanglement generated by successive passage through a cavity
Time-dependent Fr\"ohlich transformations can be used to derive an effective
Hamiltonian for a class of quantum systems with time-dependent perturbations.
We use such a transformation for a system with time-dependent atom-photon
coupling induced by the classical motion of two atoms in an inhomogeneous
electromagnetic field. We calculate the entanglement between the two atoms
resulting from their motion through a cavity as a function of their initial
position difference and velocity.Comment: 7 pages, 3 figure
Effect of low-Raman window position on correlated photon-pair generation in a chalcogenide Ge11.5As24Se64.5 nanowire
We investigated correlated photon-pair generation via spontaneous four-wave mixing in an integrated chalcogenideGe11.5As24Se64.5photonicnanowire. The coincidence to accidental ratio, a key measurement for the quality of correlated photon-pair sources, was measured to be only 0.4 when the photon pairs were generated at 1.9 THz detuning from the pump frequency due to high spontaneous Raman noise in this regime. However, the existence of a characteristic low-Raman window at around 5.1âTHz in this material's Raman spectrum and dispersion engineering of the nanowire allowed us to generate photon pairs with a coincidence to accidental ratio of 4.5, more than 10 times higher than the 1.9 THz case. Through comparing the results with those achieved in chalcogenide As2S3waveguides which also exhibit a low Raman-window but at a larger detuning of 7.4 THz, we find that the position of the characteristic low-Raman window plays an important role on reducing spontaneous Raman noise because the phonon population is higher at smaller detuning. Therefore the ultimate solution for Raman noise reduction in Ge11.5As24Se64.5 is to generate photon pairs outside the Raman gain band at more than 10 THz detuning
Heavy-quark meson spectrum tests of the Oktay-Kronfeld action
The Oktay-Kronfeld (OK) action extends the Fermilab improvement program for
massive Wilson fermions to higher order in suitable power-counting schemes. It
includes dimension-six and -seven operators necessary for matching to QCD
through order in HQET power counting, for
applications to heavy-light systems, and in NRQCD power
counting, for applications to quarkonia. In the Symanzik power counting of
lattice gauge theory near the continuum limit, the OK action includes all
and some terms. To assess whether the
theoretical improvement is realized in practice, we study combinations of
heavy-strange and quarkonia masses and mass splittings, designed to isolate
heavy-quark discretization effects. We find that, with one exception, the
results obtained with the tree-level-matched OK action are significantly closer
to the continuum limit than the results obtained with the Fermilab action. The
exception is the hyperfine splitting of the bottom-strange system, for which
our statistical errors are too large to draw a firm conclusion. These studies
are carried out with data generated with the tadpole-improved Fermilab and OK
actions on 500 gauge configurations from one of MILC's ~fm,
-flavor, asqtad-staggered ensembles.Comment: 12 pages, 5 figure
Dyon condensation in topological Mott insulators
We consider quantum phase transitions out of topological Mott insulators in
which the ground state of the fractionalized excitations (fermionic spinons) is
topologically non-trivial. The spinons in topological Mott insulators are
coupled to an emergent compact U(1) gauge field with a so-called "axion" term.
We study the confinement transitions from the topological Mott insulator to
broken symmetry phases, which may occur via the condensation of dyons. Dyons
carry both "electric" and "magnetic" charges, and arise naturally in this
system because the monopoles of the emergent U(1) gauge theory acquires gauge
charge due to the axion term. It is shown that the dyon condensate, in general,
induces simultaneous current and bond orders. To demonstrate this, we study the
confined phase of the topological Mott insulator on the cubic lattice. When the
magnetic transition is driven by dyon condensation, we identify the bond order
as valence bond solid order and the current order as scalar spin chirality
order. Hence, the confined phase of the topological Mott insulator is an exotic
phase where the scalar spin chirality and the valence bond order coexist and
appear via a single transition. We discuss implications of our results for
generic models of topological Mott insulators.Comment: 14 pages, accepted to the New Journal of Physic
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