High-Order Coupled Cluster Method (CCM) Calculations for Quantum Magnets with Valence-Bond Ground States

In this article, we prove that exact representations of dimer and plaquette valence-bond ket ground states for quantum Heisenberg antiferromagnets may be formed via the usual coupled cluster method (CCM) from independent-spin product (e.g. N\'eel) model states. We show that we are able to provide good results for both the ground-state energy and the sublattice magnetization for dimer and plaquette valence-bond phases within the CCM. As a first example, we investigate the spin-half $J_1$--$J_2$ model for the linear chain, and we show that we are able to reproduce exactly the dimerized ground (ket) state at $J_2/J_1=0.5$. The dimerized phase is stable over a range of values for $J_2/J_1$ around 0.5. We present evidence of symmetry breaking by considering the ket- and bra-state correlation coefficients as a function of $J_2/J_1$. We then consider the Shastry-Sutherland model and demonstrate that the CCM can span the correct ground states in both the N\'eel and the dimerized phases. Finally, we consider a spin-half system with nearest-neighbor bonds for an underlying lattice corresponding to the magnetic material CaV$_4$O$_9$ (CAVO). We show that we are able to provide excellent results for the ground-state energy in each of the plaquette-ordered, N\'eel-ordered, and dimerized regimes of this model. The exact plaquette and dimer ground states are reproduced by the CCM ket state in their relevant limits.Comment: 34 pages, 13 figures, 2 table

Contrasting species and functional beta diversity in montane ant assemblages

Aim Beta diversity describes the variation in species composition between sites and can be used to infer why different species occupy different parts of the globe. It can be viewed in a number of ways. First, it can be partitioned into two distinct patterns: turnover and nestedness. Second, it can be investigated from either a species identity or a functional-trait point of view. We aim to document for the first time how these two aspects of beta diversity vary in response to a large environmental gradient. Location Maloti-Drakensberg Mountains, southern Africa. Methods We sampled ant assemblages along an extensive elevational gradient (900–3000 m a.s.l.) twice yearly for 7 years, and collected functional-trait information related to the species’ dietary and habitat-structure preferences. We used recently developed methods to partition species and functional beta diversity into their turnover and nestedness components. A series of null models were used to test whether the observed beta diversity patterns differed from random expectations. Results Species beta diversity was driven by turnover, but functional beta diversity was composed of both turnover and nestedness patterns at different parts of the gradient. Null models revealed that deterministic processes were likely to be responsible for the species patterns but that the functional changes were indistinguishable from stochasticity. Main conclusions Different ant species are found with increasing elevation, but they tend to represent an increasingly nested subset of the available functional strategies. This finding is unique and narrows down the list of possible factors that control ant existence across elevation. We conclude that diet and habitat preferences have little role in structuring ant assemblages in montane environments and that some other factor must be driving the non-random patterns of species turnover. This finding also highlights the importance of distinguishing between different kinds of beta diversity

Dynamical study on polaron formation in a metal/polymer/metal structure

By considering a metal/polymer/metal structure within a tight-binding one-dimensional model, we have investigated the polaron formation in the presence of an electric field. When a sufficient voltage bias is applied to one of the metal electrodes, an electron is injected into the polymer chain, then a self-trapped polaron is formed at a few hundreds of femtoseconds while it moves slowly under a weak electric field (not larger than $$ V/cm). At an electric field between $1.0\times 10^4$ V/cm and $$ V/cm, the polaron is still formed, since the injected electron is bounded between the interface barriers for quite a long time. It is shown that the electric field applied at the polymer chain reduces effectively the potential barrier in the metal/polymer interface

Differential Geometry applied to Acoustics : Non Linear Propagation in Reissner Beams

Although acoustics is one of the disciplines of mechanics, its "geometrization" is still limited to a few areas. As shown in the work on nonlinear propagation in Reissner beams, it seems that an interpretation of the theories of acoustics through the concepts of differential geometry can help to address the non-linear phenomena in their intrinsic qualities. This results in a field of research aimed at establishing and solving dynamic models purged of any artificial nonlinearity by taking advantage of symmetry properties underlying the use of Lie groups. The geometric constructions needed for reduction are presented in the context of the "covariant" approach.Comment: Submitted to GSI2013 - Geometric Science of Informatio

Infinitesimal and local convexity of a hypersurface in a semi-Riemannian manifold

Given a Riemannian manifold M and a hypersurface H in M, it is well known that infinitesimal convexity on a neighborhood of a point in H implies local convexity. We show in this note that the same result holds in a semi-Riemannian manifold. We make some remarks for the case when only timelike, null or spacelike geodesics are involved. The notion of geometric convexity is also reviewed and some applications to geodesic connectedness of an open subset of a Lorentzian manifold are given.Comment: 14 pages, AMSLaTex, 2 figures. v2: typos fixed, added one reference and several comments, statement of last proposition correcte

Foreground removal from CMB temperature maps using an MLP neural network

One of the main obstacles in extracting the Cosmic Microwave Background (CMB) signal from observations in the mm-submm range is the foreground contamination by emission from galactic components: mainly synchrotron, free-free and thermal dust emission. Due to the statistical nature of the intrinsic CMB signal it is essential to minimize the systematic errors in the CMB temperature determinations. Following the available knowledge of the spectral behavior of the galactic foregrounds simple, power law-like spectra have been assumed. The feasibility of using a simple neural network for extracting the CMB temperature signal from the combined CMB and foreground signals has been investigated. As a specific example, we have analysed simulated data, like that expected from the ESA Planck Surveyor mission. A simple multilayer perceptron neural network with 2 hidden layers can provide temperature estimates, over more than 80 percent of the sky, that are to a high degree uncorrelated with the foreground signals. A single network will be able to cover the dynamic range of the Planck noise level over the entire sky.Comment: Accepted for publication in Astrophysics and Space Scienc

Convex domains of Finsler and Riemannian manifolds

A detailed study of the notions of convexity for a hypersurface in a Finsler manifold is carried out. In particular, the infinitesimal and local notions of convexity are shown to be equivalent. Our approach differs from Bishop's one in his classical result (Bishop, Indiana Univ Math J 24:169-172, 1974) for the Riemannian case. Ours not only can be extended to the Finsler setting but it also reduces the typical requirements of differentiability for the metric and it yields consequences on the multiplicity of connecting geodesics in the convex domain defined by the hypersurface.Comment: 22 pages, AMSLaTex. Typos corrected, references update

Quantum magnetism in two dimensions: From semi-classical N\'eel order to magnetic disorder

This is a review of ground-state features of the s=1/2 Heisenberg antiferromagnet on two-dimensional lattices. A central issue is the interplay of lattice topology (e.g. coordination number, non-equivalent nearest-neighbor bonds, geometric frustration) and quantum fluctuations and their impact on possible long-range order. This article presents a unified summary of all 11 two-dimensional uniform Archimedean lattices which include e.g. the square, triangular and kagome lattice. We find that the ground state of the spin-1/2 Heisenberg antiferromagnet is likely to be semi-classically ordered in most cases. However, the interplay of geometric frustration and quantum fluctuations gives rise to a quantum paramagnetic ground state without semi-classical long-range order on two lattices which are precisely those among the 11 uniform Archimedean lattices with a highly degenerate ground state in the classical limit. The first one is the famous kagome lattice where many low-lying singlet excitations are known to arise in the spin gap. The second lattice is called star lattice and has a clear gap to all excitations. Modification of certain bonds leads to quantum phase transitions which are also discussed briefly. Furthermore, we discuss the magnetization process of the Heisenberg antiferromagnet on the 11 Archimedean lattices, focusing on anomalies like plateaus and a magnetization jump just below the saturation field. As an illustration we discuss the two-dimensional Shastry-Sutherland model which is used to describe SrCu2(BO3)2.Comment: This is now the complete 72-page preprint version of the 2004 review article. This version corrects two further typographic errors (three total with respect to the published version), see page 2 for detail

Cytokine Expression by Inflammatory Cells Obtained from the Spinal Cords of Lewis Rats with Experimental Autoimmune Encephalomyelitis Induced by Inoculation with Myelin Basic Protein and Adjuvants

Inflammatory cells were obtained from the spinal cords of rats with acute experimental autoimmune encephalomyelitis EAE induced by inoculation with myelin basic protein MBP and adjuvants. Reverse transcriptase-polymerase chain reaction RT-PCR was used to investigate the expression of mRNA for interleukin-2 IL-2 , IL-4, IL-10 and interferon-gamma (IFN-gamma) by cells from groups of rats studied 10-21 days after inoculation. On all days of study, the inflammatory cells, which were predominantly lymphocytes, expressed mRNA for IL-2, IL-4, IL-10 and IFN-gamma. In the mRNA from normal rat spinal cord tissue, there was little expression of cytokine mRNA. Cells from a short-term MBP-reactive T cell line expressed all the cytokines. Densitometry was used to measure the products of PCR, to assess the expression of each cytokine relative to that of beta-actin. IL-2 mRNA was expressed throughout the course of disease and reached a peak on day 18, during late clinical recovery. IFN-gamma was expressed throughout the course of the disease and was also high during late recovery. IL-4 mRNA was present in the spinal cord throughout the course of the disease, with a slight rise during late recovery. Relative expression of IL-10 rose to a peak on days 17-19, during late recovery from clinical disease. This study indicates that IL-2, IL-4, IL-10 and IFN-gamma are expressed by inflammatory cells in the spinal cord in EAE, with the relative expression of all cytokines being high during late clinical recovery