Thesis (PhD)--Stellenbosch University, 2001. / 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. / AFRIKAANSE OPSOMMING: In hierdie tesis, gee ons 'n oorsig van sisteme met wanorde, waar ons konsentreer op teoretiese
berekeningsmetodes wat in die veld gebruik word. Eerstens bespreek ons die algemene eienskappe
van sisteme met wanorde en verskillende modelle en hoeveelhede wat gebruik word in die studie
van hierdie sisteme, voordat ons die berekeningsmetodes beskryf wat gebruik word om die bogenoemde
hoeveelhede te ondersoek. Hierdie berekeningstegnieke sluit in die fase formalisme wat
in een dimensie gebruik word, asook die skalingsbenadering en veldteoretiese metodes wat lei
tot nie-lineêr u-modelle in hoër dimensies. Ons voer in 'n komplementere effektiewe veldeteorie
gebaseer op die logaritmiese afgeleide van die golffunksie, en wys hoe hoeveelhede van belang
met hierdie metode bereken word. As 'n voorbeeld, word die effektiewe veldetoerie toegepas op
'n een dimensionele sisteem met 'n Gauss verdeling. Die gemiddelde digtheid van toestande,
die gemiddelde 2-punt korrelator en die gemiddelde geleidingsvermoë word bereken in 'n swak
wanorde saalpunt benadering en in 'n sterk wanorde duale benadering. Hierdie resultate word
dan numeries bereken, en in die geval van die digtheid van toestande vergelyk met die eksakte
resultaat.
| Identifer | oai:union.ndltd.org:netd.ac.za/oai:union.ndltd.org:sun/oai:scholar.sun.ac.za:10019.1/52253 |
| Date | 12 1900 |
| Creators | Van Biljon, Andrew |
| Contributors | Scholtz, F. G., Geyer, H. B., Stellenbosch University. Faculty of Science. Dept. of Physics . |
| Publisher | Stellenbosch : Stellenbosch University |
| Source Sets | South African National ETD Portal |
| Language | en_ZA |
| Detected Language | Unknown |
| Type | Thesis |
| Format | 102 p. : ill. |
| Rights | Stellenbosch University |
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