Properties of quasinormal modes in open systems.

by Tong Shiu Sing Dominic. === Parallel title in Chinese characters. === Thesis (Ph.D.)--Chinese University of Hong Kong, 1995. === Includes bibliographical references (leaves 236-241). === Acknowledgements --- p.iv === Abstract --- p.v === Chapter 1 --- Open Systems and Quasinormal Modes --- p.1...

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Other Authors: Tong, Shiu Sing Dominic.
Format: Others
Language:English
Published: Chinese University of Hong Kong 1995
Subjects:
Online Access:http://library.cuhk.edu.hk/record=b5888332
http://repository.lib.cuhk.edu.hk/en/item/cuhk-318332
id ndltd-cuhk.edu.hk-oai-cuhk-dr-cuhk_318332
record_format oai_dc
collection NDLTD
language English
format Others
sources NDLTD
topic Wave equation
Perturbation (Quantum dynamics)
Inner product space
Hilbert space
spellingShingle Wave equation
Perturbation (Quantum dynamics)
Inner product space
Hilbert space
Properties of quasinormal modes in open systems.
description by Tong Shiu Sing Dominic. === Parallel title in Chinese characters. === Thesis (Ph.D.)--Chinese University of Hong Kong, 1995. === Includes bibliographical references (leaves 236-241). === Acknowledgements --- p.iv === Abstract --- p.v === Chapter 1 --- Open Systems and Quasinormal Modes --- p.1 === Chapter 1.1 --- Introduction --- p.1 === Chapter 1.1.1 --- Non-Hermitian Systems --- p.1 === Chapter 1.1.2 --- Optical Cavities as Open Systems --- p.3 === Chapter 1.1.3 --- Outline of this Thesis --- p.6 === Chapter 1.2 --- Simple Models of Open Systems --- p.10 === Chapter 1.3 --- Contributions of the Author --- p.14 === Chapter 2 --- Completeness and Orthogonality --- p.16 === Chapter 2.1 --- Introduction --- p.16 === Chapter 2.2 --- Green's Function of the Open System --- p.19 === Chapter 2.3 --- High Frequency Behaviour of the Green's Function --- p.24 === Chapter 2.4 --- Completeness of Quasinormal Modes --- p.29 === Chapter 2. 5 --- Method of Projection --- p.31 === Chapter 2.5.1 --- Problems with the Usual Method of Projection --- p.31 === Chapter 2.5.2 --- Modified Method of Projection --- p.33 === Chapter 2.6 --- Uniqueness of Representation --- p.38 === Chapter 2.7 --- Definition of Inner Product and Quasi-Stationary States --- p.39 === Chapter 2.7.1 --- Orthogonal Relation of Quasinormal Modes --- p.39 === Chapter 2.7.2 --- Definition of Hilbert Space and State Vectors --- p.41 === Chapter 2.8 --- Hermitian Limits --- p.43 === Chapter 2.9 --- Numerical Examples --- p.45 === Chapter 3 --- Time-Independent Perturbation --- p.58 === Chapter 3.1 --- Introduction --- p.58 === Chapter 3.2 --- Formalism --- p.60 === Chapter 3.2.1 --- Expansion of the Perturbed Quasi-Stationary States --- p.60 === Chapter 3.2.2 --- Formal Solution --- p.62 === Chapter 3.2.3 --- Perturbative Series --- p.66 === Chapter 3.3 --- Diagrammatic Perturbation --- p.70 === Chapter 3.3.1 --- Series Representation of the Green's Function --- p.70 === Chapter 3.3.2 --- Eigenfrequencies --- p.73 === Chapter 3.3.3 --- Eigenfunctions --- p.75 === Chapter 3.4 --- Numerical Examples --- p.77 === Chapter 4 --- Method of Diagonization --- p.81 === Chapter 4.1 --- Introduction --- p.81 === Chapter 4.2 --- Formalism --- p.82 === Chapter 4.2.1 --- Matrix Equation with Non-unique Solution --- p.82 === Chapter 4.2.2 --- Matrix Equation with a Unique Solution --- p.88 === Chapter 4.3 --- Numerical Examples --- p.91 === Chapter 5 --- Evolution of the Open System --- p.97 === Chapter 5.1 --- Introduction --- p.97 === Chapter 5.2 --- Evolution with Arbitrary Initial Conditions --- p.99 === Chapter 5.3 --- Evolution with the Outgoing Plane Wave Condition --- p.106 === Chapter 5.3.1 --- Evolution Inside the Cavity --- p.106 === Chapter 5.3.2 --- Evolution Outside the Cavity --- p.110 === Chapter 5.4 --- Physical Implications --- p.112 === Chapter 6 --- Time-Dependent Perturbation --- p.114 === Chapter 6.1 --- Introduction --- p.114 === Chapter 6.2 --- Inhomogeneous Wave Equation --- p.117 === Chapter 6.3 --- Perturbative Scheme --- p.120 === Chapter 6.4 --- Energy Changes due to the Perturbation --- p.128 === Chapter 6.5 --- Numerical Examples --- p.131 === Chapter 7 --- Adiabatic Approximation --- p.150 === Chapter 7.1 --- Introduction --- p.150 === Chapter 7.2 --- The Effect of a Varying Refractive Index --- p.153 === Chapter 7.3 --- Adiabatic Expansion --- p.156 === Chapter 7.4 --- Numerical Examples --- p.167 === Chapter 8 --- Generalization of the Formalism --- p.176 === Chapter 8. 1 --- Introduction --- p.176 === Chapter 8.2 --- Generalization of the Orthogonal Relation --- p.180 === Chapter 8.3 --- Evolution with the Outgong Wave Condition --- p.183 === Chapter 8.4 --- Uniform Convergence of the Series Representation --- p.193 === Chapter 8.5 --- Uniqueness of Representation --- p.200 === Chapter 8.6 --- Generalization of Standard Calculations --- p.202 === Chapter 8.6.1 --- Time-Independent Perturbation --- p.203 === Chapter 8.6.2 --- Method of Diagonization --- p.206 === Chapter 8.6.3 --- Remarks on Dynamical Calculations --- p.208 === Appendix A --- p.209 === Appendix B --- p.213 === Appendix C --- p.225 === Appendix D --- p.231 === Appendix E --- p.234 === References --- p.236
author2 Tong, Shiu Sing Dominic.
author_facet Tong, Shiu Sing Dominic.
title Properties of quasinormal modes in open systems.
title_short Properties of quasinormal modes in open systems.
title_full Properties of quasinormal modes in open systems.
title_fullStr Properties of quasinormal modes in open systems.
title_full_unstemmed Properties of quasinormal modes in open systems.
title_sort properties of quasinormal modes in open systems.
publisher Chinese University of Hong Kong
publishDate 1995
url http://library.cuhk.edu.hk/record=b5888332
http://repository.lib.cuhk.edu.hk/en/item/cuhk-318332
_version_ 1718979592089239552
spelling ndltd-cuhk.edu.hk-oai-cuhk-dr-cuhk_3183322019-02-19T03:53:58Z Properties of quasinormal modes in open systems. Wave equation Perturbation (Quantum dynamics) Inner product space Hilbert space by Tong Shiu Sing Dominic. Parallel title in Chinese characters. Thesis (Ph.D.)--Chinese University of Hong Kong, 1995. Includes bibliographical references (leaves 236-241). Acknowledgements --- p.iv Abstract --- p.v Chapter 1 --- Open Systems and Quasinormal Modes --- p.1 Chapter 1.1 --- Introduction --- p.1 Chapter 1.1.1 --- Non-Hermitian Systems --- p.1 Chapter 1.1.2 --- Optical Cavities as Open Systems --- p.3 Chapter 1.1.3 --- Outline of this Thesis --- p.6 Chapter 1.2 --- Simple Models of Open Systems --- p.10 Chapter 1.3 --- Contributions of the Author --- p.14 Chapter 2 --- Completeness and Orthogonality --- p.16 Chapter 2.1 --- Introduction --- p.16 Chapter 2.2 --- Green's Function of the Open System --- p.19 Chapter 2.3 --- High Frequency Behaviour of the Green's Function --- p.24 Chapter 2.4 --- Completeness of Quasinormal Modes --- p.29 Chapter 2. 5 --- Method of Projection --- p.31 Chapter 2.5.1 --- Problems with the Usual Method of Projection --- p.31 Chapter 2.5.2 --- Modified Method of Projection --- p.33 Chapter 2.6 --- Uniqueness of Representation --- p.38 Chapter 2.7 --- Definition of Inner Product and Quasi-Stationary States --- p.39 Chapter 2.7.1 --- Orthogonal Relation of Quasinormal Modes --- p.39 Chapter 2.7.2 --- Definition of Hilbert Space and State Vectors --- p.41 Chapter 2.8 --- Hermitian Limits --- p.43 Chapter 2.9 --- Numerical Examples --- p.45 Chapter 3 --- Time-Independent Perturbation --- p.58 Chapter 3.1 --- Introduction --- p.58 Chapter 3.2 --- Formalism --- p.60 Chapter 3.2.1 --- Expansion of the Perturbed Quasi-Stationary States --- p.60 Chapter 3.2.2 --- Formal Solution --- p.62 Chapter 3.2.3 --- Perturbative Series --- p.66 Chapter 3.3 --- Diagrammatic Perturbation --- p.70 Chapter 3.3.1 --- Series Representation of the Green's Function --- p.70 Chapter 3.3.2 --- Eigenfrequencies --- p.73 Chapter 3.3.3 --- Eigenfunctions --- p.75 Chapter 3.4 --- Numerical Examples --- p.77 Chapter 4 --- Method of Diagonization --- p.81 Chapter 4.1 --- Introduction --- p.81 Chapter 4.2 --- Formalism --- p.82 Chapter 4.2.1 --- Matrix Equation with Non-unique Solution --- p.82 Chapter 4.2.2 --- Matrix Equation with a Unique Solution --- p.88 Chapter 4.3 --- Numerical Examples --- p.91 Chapter 5 --- Evolution of the Open System --- p.97 Chapter 5.1 --- Introduction --- p.97 Chapter 5.2 --- Evolution with Arbitrary Initial Conditions --- p.99 Chapter 5.3 --- Evolution with the Outgoing Plane Wave Condition --- p.106 Chapter 5.3.1 --- Evolution Inside the Cavity --- p.106 Chapter 5.3.2 --- Evolution Outside the Cavity --- p.110 Chapter 5.4 --- Physical Implications --- p.112 Chapter 6 --- Time-Dependent Perturbation --- p.114 Chapter 6.1 --- Introduction --- p.114 Chapter 6.2 --- Inhomogeneous Wave Equation --- p.117 Chapter 6.3 --- Perturbative Scheme --- p.120 Chapter 6.4 --- Energy Changes due to the Perturbation --- p.128 Chapter 6.5 --- Numerical Examples --- p.131 Chapter 7 --- Adiabatic Approximation --- p.150 Chapter 7.1 --- Introduction --- p.150 Chapter 7.2 --- The Effect of a Varying Refractive Index --- p.153 Chapter 7.3 --- Adiabatic Expansion --- p.156 Chapter 7.4 --- Numerical Examples --- p.167 Chapter 8 --- Generalization of the Formalism --- p.176 Chapter 8. 1 --- Introduction --- p.176 Chapter 8.2 --- Generalization of the Orthogonal Relation --- p.180 Chapter 8.3 --- Evolution with the Outgong Wave Condition --- p.183 Chapter 8.4 --- Uniform Convergence of the Series Representation --- p.193 Chapter 8.5 --- Uniqueness of Representation --- p.200 Chapter 8.6 --- Generalization of Standard Calculations --- p.202 Chapter 8.6.1 --- Time-Independent Perturbation --- p.203 Chapter 8.6.2 --- Method of Diagonization --- p.206 Chapter 8.6.3 --- Remarks on Dynamical Calculations --- p.208 Appendix A --- p.209 Appendix B --- p.213 Appendix C --- p.225 Appendix D --- p.231 Appendix E --- p.234 References --- p.236 Chinese University of Hong Kong Tong, Shiu Sing Dominic. Chinese University of Hong Kong Graduate School. Division of Physics. 1995 Text bibliography print v, 241 leaves : ill. ; 30 cm. cuhk:318332 http://library.cuhk.edu.hk/record=b5888332 eng Use of this resource is governed by the terms and conditions of the Creative Commons “Attribution-NonCommercial-NoDerivatives 4.0 International” License (http://creativecommons.org/licenses/by-nc-nd/4.0/) http://repository.lib.cuhk.edu.hk/en/islandora/object/cuhk%3A318332/datastream/TN/view/Properties%20of%20quasinormal%20modes%20in%20open%20systems.jpghttp://repository.lib.cuhk.edu.hk/en/item/cuhk-318332