ETD Collection

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Author: search.filters.author.Nokwara, Nkululeko

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    Brane states and group representation theory
    (2014-01-14) Nokwara, Nkululeko
    A complete understanding of quantum gravity remains an open problem. However, the AdS/CFT correspondence which relates quantum eld theories that enjoy conformal symmetry to theories of (quantum) gravity is proving to be a useful tool in shedding light on this formidable problem. Recently developed group representation theoretic methods have proved useful in understanding the large N; but non-planar limit of N = 4 supersymmetric Yang-Mills theory. In this work, we study operators that are dual to excited giant gravitons, which corresponds to a sector of N = 4 super Yang-Mills theory that is described by a large N; but non-planar limit. After a brief review of the work done in the su (2) sector, we compute the spectrum of anomalous dimensions in the su (2) sector of the Leigh-Strassler deformed theory. The result resembles the spectrum of a shifted harmonic oscillator. We then explain how to construct restricted Schur polynomials built using both fermionic and bosonic elds which transform in the adjoint of the gauge group U (N) : We show that these operators diagonalise the free eld two point function to all orders in 1=N: As an application of our new operators, we study the action of the one-loop dilatation operator in the su (2,3) sector in a large N; but non-planar limit of N = 4 super Yang-Mills theory. As in the su (2) case, the resulting spectrum matches the spectrum of a set of decoupled oscillators. Finally, in an appendix, we study the action of the one-loop dilatation operator in an sl (2) sector of N = 4 super Yang-Mills theory. Again, the resulting spectrum matches that of a set of harmonic oscillators. In all these cases, we nd that the action of the dilatation operator is diagonalised by a double coset ansatz.
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    Optical properties of the 11-cis retinal molecule from time-dependent density functional theory
    (2010-08-30) Nokwara, Nkululeko
    Time Dependent Density Functional Theory (TDDFT) happens to be at a momentous stage of its development, paralleled by the production of powerful and very fast computers. Such a combination has made it possible to carry out abinitio studies of the ground and excited states of such large molecules. Starting with the ground state properties, TDDFT as implemented in the real space code, Octopus, was used to calculate the optical properties of the molecule. In particular, the optical absorption spectrum was computed in great agreement with experiment, but unexpected extra properties are also predicted. Short and strong laser pulses (in one case I = 1013W=cm2 and in the other case I = 1016W=cm2) were shot through the molecule theoretically and high harmonic generation (for I = 1013W=cm2) and coulomb explosion (for I = 1016W=cm2) were observed. For each of the three scenarios studied here, a QM/MM calculation was also carried out. Unfortunately, the overestimating (for ionization) Local Density Approximation (LDA) for the exchange-correlation functional was used throughout, since the more accurate exact exchange (EXX) over-burdened the eight-core machine that was used in this work.