Beyond the simple Proximity Force Approximation: geometrical effects on the non-retarded Casimir interaction

We study the geometrical corrections to the simple Proximity Force Approximation for the non-retarded Casimir force. We present analytical results for the force between objects of various shapes and substrates, and between pairs of objects. We compare the results to those from more exact numerical calculations. We treat spheres, spheroids, cylinders, cubes, cones, and wings; the analytical PFA results together with the geometrical correction factors are summarized in a table.Comment: 18 pages, 19 figures, 1 tabl

ANCSA and 1991: A Framework for Analysis

We study the geometrical corrections to the simple Proximity Force Approximation (PFA) for the non-retarded Casimir force. We extend traditional PFA in two ways: We take the whole surfaces of the objects facing each other into account, not just the curvatures at the point of closest distance; we take the thickness of the coating of coated objects into account in the formalism. We present analytical and numerical results for a sphere above a substrate, for a spherical shell above a substrate, and for two interacting spheres. We compare the results to those from a multi-polar expansion method, a method based on a more solid foundation.Original Publication: Bo E. Sernelius and C.E. Roman-Velazquez, Test of the proximity force approximation, 2009, Journal of Physics: Conference Series, (161), 012016. http://dx.doi.org/10.1088/1742-6596/161/1/012016 Copyright: Institute of Physics http://journals.iop.org/</p

Generalized Burchnall-Type Identities for Orthogonal Polynomials and Expansions

Burchnall's method to invert the Feldheim-Watson linearization formula for the Hermite polynomials is extended to all polynomial families in the Askey-scheme and its $q$-analogue. The resulting expansion formulas are made explicit for several families corresponding to measures with infinite support, including the Wilson and Askey-Wilson polynomials. An integrated version gives the possibility to give alternate expression for orthogonal polynomials with respect to a modified weight. This gives expansions for polynomials, such as Hermite, Laguerre, Meixner, Charlier, Meixner-Pollaczek and big $q$-Jacobi polynomials and big $q$-Laguerre polynomials. We show that one can find expansions for the orthogonal polynomials corresponding to the Toda-modification of the weight for the classical polynomials that correspond to known explicit solutions for the Toda lattice, i.e., for Hermite, Laguerre, Charlier, Meixner, Meixner-Pollaczek and Krawtchouk polynomials

The role of geometry on dispersive forces

The role of geometry on dispersive forces is investigated by calculating the energy between different spheroidal particles and planar surfaces, both with arbitrary dielectric properties. The energy is obtained in the non-retarded limit using a spectral representation formalism and calculating the interaction between the surface plasmons of the two macroscopic bodies. The energy is a power-law function of the separation of the bodies, where the exponent value depends on the geometrical parameters of the system, like the separation distance between bodies, and the aspect ratio among minor and major axes of the spheroid.Comment: Presneted at QFEXT05, Barcelona 2005. Submitted to J. Phys.

Hybrid Organic−Inorganic Solids That Show Shape Selectivity

Hybrid organic−inorganic solids featuring millimolar/gram concentrations of intracrystalline organic moieties and shape-selectivity are synthesized. Pure-silica zeolite beta crystals are coated with zirconia and treated in aqueous sodium hydroxide to create defects and mesoporosity within the crystalline structure. Aminopropyl organic groups are subsequently grafted onto the generated intracrystalline silanol groups. After grafting, characterization data indicate a high organic concentration localized primarily within the intracrystalline voids. Specifically, thermogravimetric analysis shows an organic loading of 0.7 mmol of NH_2/g, ^(29)Si solid-state nuclear magnetic resonance (NMR) spectra display a quantitative decrease in Q^3 silicon atoms with a corresponding resharpening of the Q^4 resonances, and N_2 adsorption data show a decrease in micropore volume to 0.10 cm^3/g. Knoevenagel condensation reactions are catalyzed by the aminopropyl-functionalized materials using differently sized aldehydes and the results show that the zirconia-protected functionalized solid have shape selective properties

Enhancement of entanglement in one-dimensional disordered systems

The pairwise quantum entanglement of sites in disordered electronic one-dimensional systems (rings) is studied. We focus on the effect of diagonal and off diagonal disorder on the concurrence $C_{ij}$ between electrons on neighbor and non neighbor sites $i,j$ as a function of band filling. In the case of diagonal disorder, increasing the degree of disorder leads to a decrease of the concurrence with respect to the ordered case. However, off-diagonal disorder produces a surprisingly strong enhancement of entanglement. This remarkable effect occurs near half filling, where the concurrence becomes up to 15% larger than in the ordered system.Comment: 21 pages, 9 figure

Dynamics of the Formation of Bright Solitary Waves of Bose-Einstein Condensates in Optical Lattices

We present a detailed description of the formation of bright solitary waves in optical lattices. To this end, we have considered a ring lattice geometry with large radius. In this case, the ring shape does not have a relevant effect in the local dynamics of the condensate, while offering a realistic set up to implement experiments with conditions usually not available with linear lattices (in particular, to study collisions). Our numerical results suggest that the condensate radiation is the relevant dissipative process in the relaxation towards a self-trapped solution. We show that the source of dissipation can be attributed to the presence of higher order dispersion terms in the effective mass approach. In addition, we demonstrate that the stability of the solitary solutions is linked with particular values of the width of the wavepacket in the reciprocal space. Our study suggests that these critical widths for stability depend on the geometry of the energy band, but are independent of the condensate parameters (momentum, atom number, etc.). Finally, the non-solitonic nature of the solitary waves is evidenced showing their instability under collisions.Comment: 7 pages, 7 figures, to appear in PR

Mechanism of Glucose Isomerization Using a Solid Lewis Acid Catalyst in Water

^1H and ^(13)C NMR spectroscopy on isotopically labeled glucose reveals that in the presence of tin-containing zeolite Sn-Beta, the isomerization reaction of glucose in water proceeds by way of an intramolecular hydride shift (see scheme) rather than proton transfer. This is the first mechanistic demonstration of Sn-Beta acting as a Lewis acid in a purely aqueous environment