Functional Relations and Bethe Ansatz for the XXZ Chain

There is an approach due to Bazhanov and Reshetikhin for solving integrable RSOS models which consists of solving the functional relations which result from the truncation of the fusion hierarchy. We demonstrate that this is also an effective means of solving integrable vertex models. Indeed, we use this method to recover the known Bethe Ansatz solutions of both the closed and open XXZ quantum spin chains with U(1) symmetry. Moreover, since this method does not rely on the existence of a pseudovacuum state, we also use this method to solve a special case of the open XXZ chain with nondiagonal boundary terms.     

Neutron diffraction and computer simulation study of liquid CS2 and CSe2

The structure factor of liquid CS₂ has been measured at ambient temperature by the 7C2 diffractometer at the Laboratoire Leon Brillouin?, Saclay, France. The result has been modelled by the reverse Monte Carlo (RMC) method. The only reported neutron diffraction measurement on liquid CSe₂ has also been investigated in detail. In both cases initial configurations for the RMC runs have been obtained by molecular dynamics simulation using a simple soft sphere potential. It has been found that the main features of experimental results have been reproduced even by this choice suggesting that the structure of these systems is almost entirely described by the excluded volume. Examination of model size dependence of results has also been carried out revealing the importance of using large simulation boxes.     

带多个形状参数的Bézier曲线

基于Bézier曲线升阶的思想,构造了带多个形状参数的Bézier曲线,它具有与Bézier曲线相同的性质.在控制顶点不变的情况下,可通过改变多个形状参数的取值调整曲线的形状.n次Bézier曲线是n次带多个形状参数的Bézier曲线的一个特例,多个形状参数可使曲线变化更灵活.     

Finite size effects in the spin-1 XXZ and supersymmetric sine-Gordon models with Dirichlet boundary conditions

Starting from the Bethe Ansatz solution of the open integrable spin-1 XXZ quantum spin chain with diagonal boundary terms, we derive a set of nonlinear integral equations (NLIEs), which we propose to describe the boundary supersymmetric sine-Gordon model BSSG⁺ with Dirichlet boundary conditions on a finite interval. We compute the corresponding boundary S matrix, and find that it coincides with the one proposed by Bajnok, Palla and Takács for the Dirichlet BSSG⁺ model. We derive a relation between the (UV) parameters in the boundary conditions and the (IR) parameters in the boundary S matrix. By computing the boundary vacuum energy, we determine a previously unknown parameter in the scattering theory. We solve the NLIEs numerically for intermediate values of the interval length, and find agreement with our analytical result for the effective central charge in the UV limit and with boundary conformal perturbation theory.     

Boundary Energy of the Open XXZ Chain from New Exact Solutions

Bethe Ansatz solutions of the open spin- integrable XXZ quantum spin chain at roots of unity with nondiagonal boundary terms containing two free boundary parameters have recently been proposed.We use these solutions to compute the boundary energy (surface energy) in the thermodynamic limit. Communicated by Vincent Rivasseau Dedicated to Daniel Arnaudon Submitted: December 6, 2005; Accepted: February 16, 2006     

Supersymmetric skyrmions in four dimensions

Possible topological solitons (skyrmions) of four-dimensional supersymmetric nonlinear σ-models are investigated. The requirements of supersymmetry limit our study to the CP¹ model. A stable soliton seems possible, but in the absence of a demonstrated lower-bound for the mass, the stability of the soliton is unproved. The semi-classical spectrum of the CP¹ skyrmion, as well as its supersymmetric extension, is studied.     

Gauge invariance versus masslessness in de Sitter spaces

The connection between gauge invariance, masslessness and null cone propagation is a flat space property which does not persist even in constant curvature geometries. In particular, we show that both the gauge invariant spin $\text{3}\text{2}$ and 2 fields in anti-de Sitter space have support inside the cone, whereas where are conformally invariant, but gauge variant, models which do propagate on the light cone. The Maxwell field in constant curvature spaces of dimension other than four also does not have null cone propagation; again there is a conformally invariant model which does.     

Carbon stable isotopes reveal complex trophic interactions in lake plankton

The lower trophic linkages in lake plankton food webs are generally described as relatively simple, even accounting for the additional complexity of potential 'microbial looping'. Crustacean zooplankton are frequently amalgamated into one trophic functional group as grazers of autotrophic production. The carbon stable isotope ratios for separated zooplankton species, particulate organic matter (POM) and phytoplankton from a number of lakes in Finland and the UK were analysed. These revealed greater complexity in trophic interactions than would otherwise be observed if the zooplankton had been represented by a mixed sample. Grazing zooplankton were usually depleted in (13)C relative to the bulk POM on which they might feed, with (13)C deviating by up to 17 per thousand There were no consistent differences between (13)C values for copepods and cladocerans. Predatory cladocerans were generally enriched by greater than 1 per thousand compared to their putative prey. We suggest that care in separating the zooplankton species for stable isotope analysis may expose otherwise undetected sources of carbon and facilitate unravelling trophic links further up the food web. Copyright 1999 John Wiley & Sons, Ltd.     

Review of AdS/CFT Integrability: An Overview

This is the introductory chapter of a review collection on integrability in the context of the AdS/CFT correspondence. In the collection, we present an overview of the achievements and the status of this subject as of the year 2010.