Anion polarizability functions in alkali halide crystals

Anion polarizabilities in alkali halide crystals are analysed as a function of interionic separation R. The anion polarizability is treated as a function of the anion and cation radii, with its partial derivatives approximated by those with respect to R for fixed cation and anion, respectively. With pressure derivatives of the ionic radii deduced from the crystal compressibility, assuming transferability among crystals, the polarizability derivatives with respect to ionic radius yield pressure derivatives of the polarizability that agree with experiment to within a factor of two. These results offer a useful means of predicting the pressure dependence of dielectric data.     

Models of environmental effects on anion polarizability

This paper deals with three different approaches to the representation of environmental effects on anion polarizability in cubic crystals of the stoichiometry MX, where M is an alkali metal and X is a halogen. Ab initio embedded cluster calculations of the variation in anion polarizability with pressure in a fixed crystal type are presented and compared with experiment. The results are then used in a scaled ab initio model used to predict further values for the pressure dependence of the in-crystal anion polarizability. This scaled model is compared with a fully empirical ‘universal’ model due to Batana et al. based on polarizability change with ionic radius [1997, Molec. Phys., 92, 1029]. The assumptions of the two models differ substantially and the central purpose of this paper is to contrast these differences and highlight their consequences for prediction. Although the empirical model typically overestimates the experimental pressure derivatives, and the ab initio calculations somewhat underestimate them, it is shown that the assumption of incompressible cations in the scaled ab initio-derived model has a firmer physical basis than the empirical picture in which all ions are compressible.     

Molecular dynamics study of the mobility in poly(butyl methacrylate) isomers

Molecular mobility is studied in poly(butyl methacrylate) isomers with molecular dynamics simulations in order to understand the role of the side chain steric hindrance on the β and δ relaxation mechanisms. The simulations suggest that in the temperature range studied the δ process is weakly influenced by the α process. Conversely, the β process seems to be significantly changed as compared with the low frequency regime. The results exposed also show evidence that the intramolecular cooperativity is higher in PnBMA than in PtBMA, which, could be related to the distance to the α-β crossover.     

Determining Knotsw and Links by Cyclic Branched Coverings

It is well known that different knots or links in the 3-sphere can have homeomorphic n-fold cyclic branched coverings. We consider the following problem: for which values of nis a knot of link determined by itsn-fold cyclic branched covering? We consider the class of hyperbolic resp.2π/n-hyperbolic links. The isometry or symmetry groups of such links are finite, and their n-fold branched coverings are hyperbolic 3-manifolds. Our main result states that if ndoes not divide the order of the finite symmetry group of such a link, then the link is determined by its n-fold branched covering. In a sense, the result is best possible; the key argument of its proof is algebraic using some basic result about finite p-groups. The main result applies, for example, to the cyclic branched coverings of the 2-bridge links; in particular, it gives a classification of the maximally symmetricD₆-manifolds which are exactly the 3-fold branched coverings of the 2-bridge links.     

The Spectral Gap of the Ferromagnetic XXZ-Chain

We prove that the spectral gap of the spin- ferromagnetic XXZ-chain with HamiltonianH=–_x S^{(1)}_xS^{(1)}_{x+1}+S^{(2)}_xS^{(2)}_{x+1}+\Delta S^{(3)}_xS^{(3)}_{x+1}, is given by -1 for all 1. This is the gap in the spectrum of the infinite chainin any of its ground states, the translation invariant ones as well asthe kink ground states, which contain an interface between an up and a down region.In particular, this shows that the lowest magnon energy is not affected by the presence of a domain wall. This surprising fact is a consequence of the SU _q (2)quantum group symmetry of the model.     

Algebraic study of chiral anomalies?

The algebraic structure of chiral anomalies ismade globally valid on non-trivial bundles by the introduction of a fixed background connection. Some of the techniques used in the study of the anomaly are improved or generalized, including a systematic way of generating towers of ??descent equations??.