More on coupling coefficients for the most degenerate representations of SO(n)

We present explicit closed-form expressions for the general group-theoretical factor appearing in the alpha-topology of a high-temperature expansion of SO(n)-symmetric lattice models. This object, which is closely related to 6j-symbols for the most degenerate representation of SO(n), is discussed in detail.Comment: 9 pages including 1 table, uses IOP macros Update of Introduction and Discussion, References adde

Scattering and absorption of ultracold atoms by nanotubes

We investigate theoretically how cold atoms, including Bose-Einstein condensates, are scattered from, or absorbed by nanotubes with a view to analysing recent experiments. In particular we consider the role of potential strength, quantum reflection, atomic interactions and tube vibrations on atom loss rates. Lifshitz theory calculations deliver a significantly stronger scattering potential than that found in experiment and we discuss possible reasons for this. We find that the scattering potential for dielectric tubes can be calculated to a good approximation using a modified pairwise summation approach, which is efficient and easily extendable to arbitrary geometries. Quantum reflection of atoms from a nanotube may become a significant factor at low temperatures, especially for non-metallic tubes. Interatomic interactions are shown to increase the rate at which atoms are lost to the nanotube and lead to non-trivial dynamics. Thermal nanotube vibrations do not significantly increase loss rates or reduce condensate fractions, but lower frequency oscillations can dramatically heat the cloud.Comment: 7 pages, 4 figure

Comparative leaf anatomy and systematics in Dendrobium, sections Aporum and Rhizobium (Orchidaceae)

The specialized leaf anatomy for species of Dendrobium within section Aporum is similar to that of species in section Rhizobium. In both sections leaves are characterized by a unifacial or nearly unifacial surface where the exposed surface is abaxial. However, leaves in section Rhizobium also feature a lacuna submerged in the mesophyll and surrounded by an adaxial epidermis. In contrast, leaves in section Aporum merely present an internal suture that divides the leaf into bilateral halves. These two sections of Dendrobium are hypothesized to be sister taxa because of synapomorphies in their foliar anatomy. A cladistic analysis performed with various anatomical characters of the leaf demonstrates that both groups are monophyletic. Little resolution was found within the anatomically and morphologically distinctive Aporum clade

Comparative leaf anatomy and systematics in Dendrobium, sections Aporum and Rhizobium (Orchidaceae)

The specialized leaf anatomy for species of Dendrobium within section Aporum is similar to that of species in section Rhizobium. In both sections leaves are characterized by a unifacial or nearly unifacial surface where the exposed surface is abaxial. However, leaves in section Rhizobium also feature a lacuna submerged in the mesophyll and surrounded by an adaxial epidermis. In contrast, leaves in section Aporum merely present an internal suture that divides the leaf into bilateral halves. These two sections of Dendrobium are hypothesized to be sister taxa because of synapomorphies in their foliar anatomy. A cladistic analysis performed with various anatomical characters of the leaf demonstrates that both groups are monophyletic. Little resolution was found within the anatomically and morphologically distinctive Aporum clade

Analytical Work in Support of the Design and Operation of Two Dimensional Self Streamlining Test Sections

A method has been developed for accurately computing the imaginary flow fields outside a flexible walled test section, applicable to lifting and non-lifting models. The tolerances in the setting of the flexible walls introduce only small levels of aerodynamic interference at the model. While it is not possible to apply corrections for the interference effects, they may be reduced by improving the setting accuracy of the portions of wall immediately above and below the model. Interference effects of the truncation of the length of the streamlined portion of a test section are brought to an acceptably small level by the use of a suitably long test section with the model placed centrally

Radio-frequency dressed lattices for ultracold alkali atoms

Ultracold atomic gases in periodic potentials are powerful platforms for exploring quantum physics in regimes dominated by many-body effects as well as for developing applications that benefit from quantum mechanical effects. Further advances face a range of challenges including the realization of potentials with lattice constants smaller than optical wavelengths as well as creating schemes for effective addressing and manipulation of single sites. In this paper we propose a dressed-based scheme for creating periodic potential landscapes for ultracold alkali atoms with the capability of overcoming such difficulties. The dressed approach has the advantage of operating in a low-frequency regime where decoherence and heating effects due to spontaneous emission do not take place. These results highlight the possibilities of atom-chip technology in the future development of quantum simulations and quantum technologies, and provide a realistic scheme for starting such an exploration

A Synopsis of Melanthiaceae (Liliales) with Focus on Character Evolution in Tribe Melanthieae

Melanthiaceae s.l. comprises five tribes: Chionographideae, Heloniadeae, Melanthieae, Parideae, and Xerophylleae—each defined by distinctive autapomorphies. The most morphologically diverse tribe Melanthieae, now with seven genera, had not been subject to rigorous phylogenetic character study prior to the current series of investigations that also include an overview of the family. Data from our publications and studies underway are here assessed and integrated, providing a useful overview of Melanthiaceae, and especially of Melanthieae. The results of parsimony analyses of ITS (nuclear ribosomal) and trnL-F (plastid) DNA sequence data correlate with potentially synapomorphic phenotypic characters for genera of Melanthieae, including habit form, rootstock type, bulb shape, inflorescence structure, indumentum type, tepa! shape, nectary morphology, and ovary position. Sequence data also correlate well with the pattern of variation in chromosome number. The molecular and morphological data support generic recircumscription in Melanthieae and also validate several generalizations concerning character evolution within the tribe, as well as among the tribes of the family

Chaos and localization in the wavefunctions of complex atoms NdI, PmI and SmI

Wavefunctions of complex lanthanide atoms NdI, PmI and SmI, obtained via multi-configuration Dirac-Fock method, are analyzed for density of states in terms of partial densities, strength functions ($F_k(E)$), number of principal components ($\xi_2(E)$) and occupancies (\lan n_\alpha \ran^E) of single particle orbits using embedded Gaussian orthogonal ensemble of one plus two-body random matrix ensembles [EGOE(1+2)]. It is seen that density of states are in general multi-modal, $F_k(E)$'s exhibit variations as function of the basis states energy and $\xi_2(E)$'s show structures arising from localized states. The sources of these departures from EGOE(1+2) are investigated by examining the partial densities, correlations between $F_k(E)$, $\xi_2(E)$ and \lan n_\alpha \ran^E and also by studying the structure of the Hamiltonian matrices. These studies point out the operation of EGOE(1+2) but at the same time suggest that weak admixing between well separated configurations should be incorporated into EGOE(1+2) for more quantitative description of chaos and localization in NdI, PmI and SmI.Comment: There are 9 figure

Sum Rules for Multi-Photon Spectroscopy of Ions in Finite Symmetry

Models describing one- and two-photon transitions for ions in crystalline environments are unified and extended to the case of parity-allowed and parity- forbidden p-photon transitions. The number of independent parameters for characterizing the polarization dependence is shown to depend on an ensemble of properties and rules which combine symmetry considerations and physical models.Comment: 16 pages, Tex fil

Analytic Treatment of Positronium Spin Splittings in Light-Front QED

We study the QED bound-state problem in a light-front hamiltonian approach. Starting with a bare cutoff QED Hamiltonian, $H_{_{B}}$, with matrix elements between free states of drastically different energies removed, we perform a similarity transformation that removes the matrix elements between free states with energy differences between the bare cutoff, $\Lambda$, and effective cutoff, \lam (\lam < \Lam). This generates effective interactions in the renormalized Hamiltonian, $H_{_{R}}$. These effective interactions are derived to order $\alpha$ in this work, with $\alpha \ll 1$. $H_{_{R}}$ is renormalized by requiring it to satisfy coupling coherence. A nonrelativistic limit of the theory is taken, and the resulting Hamiltonian is studied using bound-state perturbation theory (BSPT). The effective cutoff, \lam^2, is fixed, and the limit, 0 \longleftarrow m^2 \alpha^2\ll \lam^2 \ll m^2 \alpha \longrightarrow \infty, is taken. This upper bound on \lam^2 places the effects of low-energy (energy transfer below \lam) emission in the effective interactions in the $| e {\overline e} >$ sector. This lower bound on \lam^2 insures that the nonperturbative scale of interest is not removed by the similarity transformation. As an explicit example of the general formalism introduced, we show that the Hamiltonian renormalized to $O(\alpha)$ reproduces the exact spectrum of spin splittings, with degeneracies dictated by rotational symmetry, for the ground state through $O(\alpha^4)$. The entire calculation is performed analytically, and gives the well known singlet-triplet ground state spin splitting of positronium, $7/6 \alpha^2 Ryd$. We discuss remaining corrections other than the spin splittings and how they can be treated in calculating the spectrum with higher precision.Comment: 46 pages, latex, 3 Postscript figures included, section on remaining corrections added, title changed, error in older version corrected, cutoff placed in a windo