Superfluid-Insulator transitions of bosons on Kagome lattice at non-integer fillings

We study the superfluid-insulator transitions of bosons on the Kagome lattice at incommensurate filling factors f=1/2 and 2/3 using a duality analysis. We find that at f=1/2 the bosons will always be in a superfluid phase and demonstrate that the T_3 symmetry of the dual (dice) lattice, which results in dynamic localization of vortices due to the Aharanov-Bohm caging effect, is at the heart of this phenomenon. In contrast, for f=2/3, we find that the bosons exhibit a quantum phase transition between superfluid and translational symmetry broken Mott insulating phases. We discuss the possible broken symmetries of the Mott phase and elaborate the theory of such a transition. Finally we map the boson system to a XXZ spin model in a magnetic field and discuss the properties of this spin model using the obtained results.Comment: 10 pages, 8 figures, a few typos correcte

An extension of Saalschütz's summation theorem for the series _<i>r</i>+3F_<i>r</i>+2

The aim in this research note is to provide an extension of Saalschütz'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. Kummer’s first theorem, the classical Gauss summation theorem and the generalized Kummer summation theorem due to Lavoie et al. [Generalizations of Whipple’s theorem on the sum of a 3 F 2, J. Comput. Appl. Math. 72 (1996), pp. 293–300] 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

Designing coupled-resonator optical waveguide delay lines

We address the trade-offs among delay, loss, and bandwidth in the design of coupled-resonator optical waveguide (CROW) delay lines. We begin by showing the convergence of the transfer matrix, tight-binding, and time domain formalisms in the theoretical analysis of CROWs. From the analytical formalisms we obtain simple, analytical expressions for the achievable delay, loss, bandwidth, and a figure of merit to be used to compare delay line performance. We compare CROW delay lines composed of ring resonators, toroid resonators, Fabry-Perot resonators, and photonic crystal defect cavities based on recent experimental results reported in the literature

Valence Bond Solids and Their Quantum Melting in Hard-Core Bosons on the Kagome Lattice

Using large scale quantum Monte Carlo simulations and dual vortex theory we analyze the ground state phase diagram of hard-core bosons on the kagome lattice with nearest neighbor repulsion. In contrast to the case of a triangular lattice, no supersolid emerges for strong interactions. While a uniform superfluid prevails at half-filling, two novel solid phases emerge at densities $\rho=1/3$ and $\rho=2/3$. These solids exhibit an only partial ordering of the bosonic density, allowing for local resonances on a subset of hexagons of the kagome lattice. We provide evidence for a weakly first-order phase transition at the quantum melting point between these solid phases and the superfluid.Comment: 4 pages, 7 figure

Perfect Test of Entanglement for Two-level Systems

A 3-setting Bell-type inequality enforced by the indeterminacy relation of complementary local observables is proposed as an experimental test of the 2-qubit entanglement. The proposed inequality has an advantage of being a sufficient and necessary criterion of the separability. Therefore any entangled 2-qubit state cannot escape the detection by this kind of tests. It turns out that the orientation of the local testing observables plays a crucial role in our perfect detection of the entanglement.Comment: 4 pages, RevTe

Slip Failure of Embankment on Soft Marine Clay

The results of an investigation carried out at a site before and after the slip failure of an embankment on soft marine clay are presented. An evaluation of the possible causes for the slip failure and the remedial measures taken after the failure are also included. It appears that overstressing of the ground might have led to the movement of the soft soil. The compressible soils were subjected to an increase in stress without a comparable increase in foundation shear strength. This increase in horizontal stress resulted in the horizontal displacement of the soil as evident by the presence of the tension cracks in the fill just before slip failure occurred