Doctoral Degrees (Physics)
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Browsing Doctoral Degrees (Physics) by browse.metadata.advisor "Geyer, H. B."
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- ItemEffective 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.
- ItemNon-commutative quantum mechanics : properties of piecewise constant potentials in two dimensions(Stellenbosch : University of Stellenbosch, 2010-12) Thom, Jacobus D. (Jacobus Daniel); Scholtz, Frederik G.; Geyer, H. B.; University of Stellenbosch. Faculty of Science. Dept. of Physics.ENGLISH ABSTRACT: The aim of this thesis is threefold. Firstly, I give an overview of non-commutative quan- tum mechanics and build up a description of non-commutative piecewise constant poten- tial wells in this context. Secondly, I look at some of the stationary properties of a finite non-commutative well using the mathematical tools laid out in the first part. Lastly, I in- vestigate how non-commutativity affects the tunneling rate through a barrier. Throughout this work I give the normal commutative descriptions and results for comparsion.