Properties of quasinormal modes in open systems.

• Other Authors: Tong, Shiu Sing Dominic.
• Format: Others
• Language: English
• Published: Chinese University of Hong Kong 1995
• Subjects: Wave equation; Perturbation (Quantum dynamics); Inner product space; Hilbert space
• Online Access: http://library.cuhk.edu.hk/record=b5888332; http://repository.lib.cuhk.edu.hk/en/item/cuhk-318332

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