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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Chinese University of Hong Kong
1995
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Online Access: | http://library.cuhk.edu.hk/record=b5888332 http://repository.lib.cuhk.edu.hk/en/item/cuhk-318332 |
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Wave equation Perturbation (Quantum dynamics) Inner product space Hilbert space |
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Wave equation Perturbation (Quantum dynamics) Inner product space Hilbert space Properties of quasinormal modes in open systems. |
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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 |