Anderson localization with self-avoiding walk representation
department or school: Science, Faculty of
department or school: Physics and Astronomy, Department of
data provider: DSpace
degree campus: UBCV
creator: Suzuki, Fumika
issued: 2012-08-30T16:14:20Z
issued: 2012
related degree: Master of Science - MSc
degree grantor: University of British Columbia
description: The Green’s function contains much information about physical systems. Mathematically, the fractional moment method (FMM) developed by Aizenman and Molchanov connects the Green’s function and the transport of electrons in the Anderson model. Recently, it has been discovered that the Green’s function on a graph can be represented using self-avoiding walks on a graph, which allows us to connect localization properties in the system and graph properties. We discuss FMM in terms of the self-avoiding walks on a general graph with a small number of assumptions.
aggregated CHO: https://circle.library.ubc.ca/rest/handle/2429/43096
note: Anderson Localization with Self-Avoiding Walk Representation by Fumika Suzuki B.Sc., The University of Leeds, 2010 A THESIS SUBMITTED IN PARTIAL FULFILLMENT OF THE REQUIREMENTS FOR THE DEGREE OF MASTER OF SCIENCE in The Faculty of Graduate Studies (Physics) THE UNIVERSITY OF BRITISH COLUMBIA (Vancouver) August 2012 c© Fumika Suzuki 2012 Abstract The Green’s function contains much information about physical systems. Mathematically, the fractional moment method (FMM) developed by Aizen- man and Molchanov connects the Green’s function and the transport of electrons in the Anderson model. Recently, it has been discovered that the Green’s function on a graph can be represented using self-avoiding walks on a graph, which allows us to connect localization properties in the system and graph properties. We discuss FMM in terms of the self-avoiding walks on a general graph with a small number of assumptions. ii Table of Contents Abstract . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . ii Table of Contents . . . . . . . . . . . . . . . . . . . . . . . . . . . . iii List of Figures . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . v Acknowledgements . . . . . . . . . . . . . . . . . . . . . . . . . . . vi 1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1 1.1 The Anderson Model . . . . . . . . . . . . . . . . . . . . . . 2 1.2 Anderson Localization . . . . . . . . . . . . . . . . . . . . . . 4 1.3 Results and Open Problems . . . . . . . . . . . . . . . . . . 5 2 Localization Properties . . . . . . . . . . . . . . . . . . . . . . 8 2.1 Spectral Localization . . . . . . . . . . . . . . . . . . . . . . 8 2.2 Dynamical Localization and Transport . . . . . . . . . . . . 9 2.3 Spectral Localization and Dynamical Localization . . . . . . 10 3 Self-Avoiding Walk Representation . . . . . . . . . . . . . . 13 3.1 SAW Representation for the Green’s Function . . . . . . . . 13 3.2 Fractional Moment Bounds with SAW Representation . . . . 1…
has type: Thesis/Dissertation
date issued: 2012-11
is shown at: 10.14288/1.0073089
language: eng
degree discipline: Physics
provider: Vancouver : University of British Columbia Library
publisher: University of British Columbia
rights: Attribution-NonCommercial-NoDerivatives 4.0 International
rights URI: http://creativecommons.org/licenses/by-nc-nd/4.0/
scholar level: Graduate
type: Text
identifier URI: http://hdl.handle.net/2429/43096