Mathematical Modelling of Nano-Electronic Systems
Date
2014-12-18
Authors
Journal Title
Journal ISSN
Volume Title
Publisher
ORCID
Type
Thesis
Degree Level
Doctoral
Abstract
Double-Qdots (DQDs) are attractive in light of their potential application to quantum
computing and other electronic applications, e.g. as specialized sensors. We consider the
electronic properties of a system consisting of two quantum dots in physical proximity,
which we will refer to as the DQD. Our main goal is to derive the essential properties
of the DQD from a model that is rigorous yet numerically tractable, and largely circumvents
the complexities of an ab initio simulation. To this end we propose a class of novel
Hamiltonians that captures the dynamics of a bi-partite quantum system, wherein the
interaction is described via a convolution or a Wiener-Hopf type operator. We subsequently
describe the density of states function and derive the electronic properties of the
underlying system. Our analysis shows that the model captures a plethora of electronic
profiles which serves as evidence for the versatility of the proposed framework for DQD
channel modelling.
A massive body of mathematical physics results, dating mostly to the last half a
century, give evidence to the claim that the statistical characteristic of fluctuations in
the level structure of a quantum system provides essential information about its dynamic
properties, e.g. in some instances these statistical parameters show whether or not the
underlying classical dynamics is integrable or chaotic. Following this tradition we have
conducted statistical analysis of the data generated numerically from the model at hand.
In this way we have characterized the fine-scale fluctuations of the spectra for several
choices of the constituents. In conclusion, we have found that the model is versatile
enough to produce several statistically distinct types of level structure. In particular,
the model is capable of reproducing very complex level structures, such as those of the
resonant microwave cavities that have been obtained experimentally in the 1990s
Description
Keywords
Qdot • double-Qdot channel • composite quantum system • nanoelectronics
Citation
Degree
Doctor of Philosophy (Ph.D.)
Department
Mathematics and Statistics
Program
Mathematics