Browsing by Author "Van Biljon, Andrew"

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    A renormalization group approach to disordered systems from supersymmetry with application to localization - delocalization transitions
    (Stellenbosch : Stellenbosch University, 1997) Van Biljon, Andrew; Stellenbosch University. Faculty of . Dept. of .
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    Aspects of quantum field theories
    (Stellenbosch : Stellenbosch University, 1997) Van Biljon, Andrew; Scholtz, Frederik G.; Stellenbosch University. Faculty of Science. Department of Physics.
    ENGLISH ABSTRACT: In this study project we give a general introduction to quantum field theories. In the first chapter we revise the operator formalism of quantum mechanics as well as the second quantization scheme that is used to describe many-particle systems. In the second chapter we develop the idea of path integrals within a quantum mechanics framework. We then apply path integral formalism developed in chapter two to introduce quantum field theories. We describe a field theory for scalar fields in chapter three and then a field theory for fermion fields in chapter four as well as the renormalization techniques in chapter five. In chapter six we show how scattering amplitudes are related to Green's functions which are derived from the path integral formalism. In the last chapter we give a brief introduction to gauge field theories.
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    Effective field theories for disordered systems from the logarithmic derivative of the wave-function
    (Stellenbosch : Stellenbosch University, 2001-12) Van Biljon, Andrew; Scholtz, Frederik G.; Geyer, H. B.; Stellenbosch University. Faculty of Science. Dept. of Physics .
    ENGLISH ABSTRACT: In this dissertation, we give an overview of disordered systems, where we concentrate on the theoretical calculation techniques used in this field. We first discuss the general properties of disordered systems and the different models and quantities used in the study of these systems, before describing calculation techniques used to investigate the quantities introduced. These calculation techniques include the phase formalism method used one dimension, as well as the scaling approach and field theoretic approaches leading to non-linear c-models in higher dimensions. We then introduce a complementary effective field theoretic approach based on the logarithmic derivative of the wave-function, and show how the quantities of interest are calculated using this method. As an example, the effective field theory is applied to one dimensional systems with Gaussian disorder. The average density of states, the average 2-point correlator and the conductivity are calculated in a weak disorder saddle-point approximation and in strong disorder duality approximation. These results are then calculated numerically and in the case of the density of states compared to the exact result.