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Clarkson C.,University of Cape Town | Ellis G.F.R.,University of Cape Town | Faltenbacher A.,University of the Western Cape | Maartens R.,University of the Western Cape | And 5 more authors.
Monthly Notices of the Royal Astronomical Society | Year: 2012

Light from 'point sources' such as supernovae is observed with a beam width of the order of the sources' size - typically less than 1au. Such a beam probes matter and curvature distributions that are very different from coarse-grained representations in N-body simulations or perturbation theory, which are smoothed on scales much larger than 1au. The beam typically travels through unclustered dark matter and hydrogen with a mean density much less than the cosmic mean, and through dark matter haloes and hydrogen clouds. Using N-body simulations, as well as a Press-Schechter approach, we quantify the density probability distribution as a function of beam width and show that, even for Gpc-length beams of 500kpc diameter, most lines of sight are significantly underdense. From this we argue that modelling the probability distribution for au-diameter beams is absolutely critical. Standard analyses predict a huge variance for such tiny beam sizes, and non-linear corrections appear to be non-trivial. It is not even clear whether underdense regions lead to dimming or brightening of sources, owing to the uncertainty in modelling the expansion rate which we show is the dominant contribution. By considering different reasonable approximations which yield very different cosmologies, we argue that modelling ultra-narrow beams accurately remains a critical problem for precision cosmology. This could appear as a discordance between angular diameter and luminosity distances when comparing supernova observations to baryon acoustic oscillations or cosmic microwave background distances. © 2012 The Authors Monthly Notices of the Royal Astronomical Society © 2012 RAS. Source

Sheikhan A.,National Institute for Theoretical Physics | Snyman I.,University of Witwatersrand
Physical Review B - Condensed Matter and Materials Physics | Year: 2012

We theoretically study a charge qubit interacting with electrons in a semi-infinite one-dimensional wire. The system displays the physics of the Fermi edge singularity. Our results generalize known results for the Fermi edge system to the regime where excitations induced by the qubit can resolve the spatial structure of the scattering region. We find resonant features in the qubit tunneling rate as a function of the qubit level splitting. They occur at integer multiples of hv F/l. Here v F is the Fermi velocity of the electrons in the wire, and l is the distance from the tip of the wire to the point where it interacts with the qubit. These features are due to the constructive interference of the amplitudes for creating single coherent left- or right-moving charge fluctuation (plasmon) in the electron gas. As the coupling between the qubit and the wire is increased, the resonances are washed out. This is a clear signature of the increasingly violent Fermi sea shake-up, associated with the creation of many plasmons whose individual energies are too low to meet the resonance condition. © 2012 American Physical Society. Source

Andrew R.C.,University of Pretoria | Mapasha R.E.,University of Pretoria | Ukpong A.M.,University of Pretoria | Chetty N.,University of Pretoria | Chetty N.,National Institute for Theoretical Physics
Physical Review B - Condensed Matter and Materials Physics | Year: 2012

We present an equation of state (EOS) that describes how the hydrostatic change in surface area is related to two-dimensional in-plane pressure (F) and yields the measure of a material's resilience to isotropic stretching (the layer modulus γ) as one of its fit parameters. We give results for the monolayer systems of graphene and boronitrene, and we also include results for Si, Ge, GeC, and SiC in the isostructural honeycomb structure for comparison. Our results show that, of the honeycomb structures, graphene is the most resilient to stretching with a value of γ C = 206.6 N m -1, second is boronitrene with γ BN = 177.0 N m -1, followed by γ SiC = 116.5 N m -1, γ GeC = 101.0 N m -1, γ Si = 44.5 N m -1, and γ Ge = 29.6 N m -1. We calculate the Young's and shear moduli from the elastic constants and find that, in general, they rank according to the layer modulus. We also find that the calculated layer modulus matches the one obtained from the EOS. We use the EOS to predict the isotropic intrinsic strength of the various systems and find that, in general, the intrinsic stresses also rank according to the layer modulus. Graphene and boronitrene have comparable strengths with intrinsic stresses of 29.4 and 26.0 N m -1, respectively. We considered four graphene allotropes including pentaheptite and graphdiyne and find that pentaheptite has a value for γ comparable to graphene. We find a phase transition from graphene to graphdiyne at F = -7.0 N m -1. We also consider bilayer, trilayer, and four-layered graphene and find that the addition of extra layers results in a linear dependence of γ with F. © 2012 American Physical Society. Source

Snyman I.,University of Witwatersrand | Snyman I.,National Institute for Theoretical Physics
Physical Review B - Condensed Matter and Materials Physics | Year: 2013

We study spatial correlations in the ground state of a one-dimensional electron gas coupled to a dynamic quantum impurity. The system displays a nontrivial many-body effect known as the Fermi edge singularity: transitions between discrete internal states of the impurity have a power-law dependence on the internal energies of the impurity states. We present compact formulas for the static current-current correlator and the pair-correlation function. These reveal that spatial correlations induced by the impurity decay slowly (as the third inverse power of distance) and have a power-law energy dependence, characteristic of the Fermi edge singularity. © 2013 American Physical Society. Source

Obodo K.O.,University of Pretoria | Chetty N.,University of Pretoria | Chetty N.,National Institute for Theoretical Physics
Journal of Physics Condensed Matter | Year: 2013

The electronic structure and properties of protactinium and its oxides (PaO and PaO2) have been studied within the framework of the local density approximation (LDA), the Perdew-Burke-Ernzerhof generalized gradient approximation [GGA(PBE)], LDA + U and GGA(PBE) + U implementations of density functional theory. The dependence of selected observables of these materials on the effective U parameter has been investigated in detail. The examined properties include lattice constants, bulk moduli, the effect of charge density distributions, the hybridization of the 5f orbital and the energy of formation for PaO and PaO2. The LDA gives better agreement with experiment for the bulk modulus than the GGA for Pa but the GGA gives better structural properties. We found that PaO is metallic and PaO2 is a Mott-Hubbard insulator. This is consistent with observations for the other actinide oxides. We discover that GGA and LDA incorrectly give metallic behavior for PaO 2. The GGA(PBE) + U calculated indirect band gap of 3.48 eV reported for PaO2 is a prediction and should stimulate further studies of this material. © 2013 IOP Publishing Ltd. Source

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