Optical surface modes of lattice vibrations

Two simple methods, based on simple crystal models, for estimating the longitudinal optical surface vibration mode frequencies which lie in a LALO gap are examined. One method consists of deriving and solving a single-variable equation for the surface mode frequency, which depends only on the experimental bulk dispersion curves. The other method consists of fitting the known dispersion curves of a simple one-dimensional model, for which the optical surface mode frequency is given by a simple expression, to experimental bulk dispersion curves of more complex crystals. The results are compared with detailed theoretical surface mode calculations. The latter method is found to give better estimates.     

Universal multiplicity hypothesis of QCD: Bounds on quark gluon coupling,quark mass and confinement region

Assuming the validity of the universal multiplicity hypothesis of quantum chromodynamics, we estimate bounds on quark gluon coupling (α_S) and quark mass (m) from the experimental data on charged hadron multiplicities. We obtain 0.3 < α_S < 0.5 and m ≈ 100 MeV. Our analysis also suggests the universal quark confinement region to be ≈ O (m_π^?1). Comparison with experiment is made for both the hadronic and leptonic induced reactions.     

Quantum chromodynamics corrections to polarised deep-inelastic electron-nucleon scattering

Quantum chromodynamics corrections to orderα _s (the running coupling constant), using the quark-parton approach are calculated for the spin-dependent structure functions in deep-inelastic polarised electron-nucleon scattering. Consequences of these corrections for the Bjorken sum rule and the asymmetry in the case of longitudinally polarised (with respect to the beam) nucleons is discussed which could provide possible tests of quantum chromodynamics. Comparison of our results with the moments of the flavour non-singlet contribution to the structure functions obtained using operator product expansion is also given. An erratum to this article is available at .     

Explicit cosmological coarse graining via spatial averaging

The present matter density of the Universe, while highly inhomogeneous on small scales, displays approximate homogeneity on large scales. We propose that whereas it is justified to use the Friedmann–Lemaître–Robertson–Walker (FLRW) line element (which describes an exactly homogeneous and isotropic universe) as a template to construct luminosity distances in order to compare observations with theory, the evolution of the scale factor in such a construction must be governed not by the standard Einstein equations for the FLRW metric, but by the modified Friedmann equations derived by Buchert (Gen Relat Gravit 32:105, 2000; 33:1381, 2001) in the context of spatial averaging in Cosmology. Furthermore, we argue that this scale factor, defined in the spatially averaged cosmology, will correspond to the effective FLRW metric provided the size of the averaging domain coincides with the scale at which cosmological homogeneity arises. This allows us, in principle, to compare predictions of a spatially averaged cosmology with observations, in the standard manner, for instance by computing the luminosity distance versus red-shift relation. The predictions of the spatially averaged cosmology would in general differ from standard FLRW cosmology, because the scale-factor now obeys the modified FLRW equations. This could help determine, by comparing with observations, whether or not cosmological inhomogeneities are an alternative explanation for the observed cosmic acceleration.     

Cosmic inhomogeneities and averaged cosmological dynamics

If general relativity (GR) describes the expansion of the Universe, the observed cosmic acceleration implies the existence of a "dark energy." However, while the Universe is on average homogeneous on large scales, it is inhomogeneous on smaller scales. While GR governs the dynamics of the inhomogeneous Universe, the averaged homogeneous Universe obeys modified Einstein equations. Can such modifications alone explain the acceleration? For a simple generic model with realistic initial conditions, we show the answer to be "no." Averaging effects negligibly influence the cosmological dynamics.     

Haldane-like antiferromagnetic spin chain in the large anisotropy limit

We consider the one dimensional, periodic spin chain with N sites, similar to the one studied by Haldane [1], however in the opposite limit of very large anisotropy and small nearest neighbour, anti-ferromagnetic exchange coupling between the spins, which are of large magnitude s. For a chain with an even number of sites we show that actually the ground state is non-degenerate and given by a superposition of the two Neél states, due to quantum spin tunnelling. With an odd number of sites, the Neél state must necessarily contain a soliton. The position of the soliton is arbitrary thus the ground state is N-fold degenerate. This set of states reorganizes into a band. We show that this occurs at order 2s in perturbation theory. The ground state is non-degenerate for integer spin, but degenerate for half-odd integer spin as is required by Kramers' theorem [18].     

Self-energy of a charge near a metal surface

A quantum mechanical expression for the self-energy of a charged particle near a metal surface has been derived. The expression incorporates the interaction of the charge with the surface and bulk plasmons including their dispersions in the hydrodynamic model. It is found that the inclusion of the plasmons dispersions gives result for the saturated value of the image potential for copper closer to experiment.     

Constant current coulometric method for the determination of uranium in active process solutions

The determination of uranium in the range of 2.5–5 mg by constant current coulometry is described. The procedure is based on the modified version of the DAVIES—GRAY method, wherein uranium, after the reduction step, is oxidized by adding a known amount of potassium dichromate, and the excess of dichromate is determined by titration with Fe²⁺ solution. Fe²⁺ ions needed for the titration are generated in situ with 100% current efficiency by electrolytic reduction of Fe³⁺. The method is found to be accurate with a coefficient of variation better than 0.2%.