Wong Chun Wing. / "August 2002." / Thesis (Ph.D.)--Chinese University of Hong Kong, 2002. / Includes bibliographical references (p. [166]-169). / Electronic reproduction. Hong Kong : Chinese University of Hong Kong, [2012] System requirements: Adobe Acrobat Reader. Available via World Wide Web. / Mode of access: World Wide Web. / Abstracts in English and Chinese.

by Ng Sik Tim. / Thesis (M.Phil.)--Chinese University of Hong Kong, 1995. / Includes bibliographical references (leaf 229). / by Ng Sik Tim. / Chapter 1 --- Introduction --- p.6 / Chapter 1.1 --- Resonances in open systems --- p.6 / Chapter 1.2 --- Descriptions of open optical systems --- p.11 / Chapter 1.3 --- The wave equations and E.M. fields --- p.17 / Chapter 2 --- The stabilization method --- p.20 / Chapter 2.1 --- Introduction --- p.20 / Chapter 2.2 --- Formalism --- p.23 / Chapter 2.2.1 --- The derivation of scattering phase shift --- p.23 / Chapter 2.2.2 --- The cumulative density of states --- p.25 / Chapter 2.3 --- Worked examples --- p.32 / Chapter 2.3.1 --- The importance of large b --- p.32 / Chapter 2.3.2 --- The comparison of different approaches --- p.35 / Chapter 2.3.3 --- Summary --- p.52 / Chapter 2.4 --- Other examples --- p.52 / Chapter 2.4.1 --- Discussions --- p.52 / Chapter 3 --- Completeness and orthogonality of QNM's --- p.64 / Chapter 3.1 --- Introduction --- p.64 / Chapter 3.2 --- QNM's of the scalar analog of electromagnetism --- p.65 / Chapter 3.3 --- The representation of Green's function --- p.66 / Chapter 3.4 --- The completeness of QNM's --- p.72 / Chapter 3.5 --- The orthogonality of QNM's --- p.73 / Chapter 3.6 --- Discussions --- p.75 / Chapter 4 --- Variational method for resonant states --- p.78 / Chapter 4.1 --- Introduction --- p.78 / Chapter 4.2 --- Formalism --- p.79 / Chapter 4.2.1 --- Complex variational method --- p.79 / Chapter 4.2.2 --- Non-linear variation --- p.82 / Chapter 4.2.3 --- Linear variation --- p.84 / Chapter 4.2.4 --- The orthogonality of approximate wave function --- p.85 / Chapter 4.3 --- Numerical examples --- p.86 / Chapter 4.3.1 --- A sketch of calculations --- p.86 / Chapter 5 --- The diagonalization method --- p.98 / Chapter 5.1 --- Introduction --- p.98 / Chapter 5.2 --- Completeness and orthogonality --- p.100 / Chapter 5.3 --- Formalism --- p.101 / Chapter 5.4 --- Numerical examples --- p.107 / Chapter 5.4.1 --- Descriptions of examples and results --- p.108 / Chapter 5.4.2 --- Summary of results --- p.131 / Chapter 5.5 --- Discussions --- p.134 / Chapter 5.5.1 --- The case with a > c --- p.134 / Chapter 5.5.2 --- A comparison with Fourier's series --- p.138 / Chapter 6 --- The Green's function method --- p.147 / Chapter 6.1 --- Formalism --- p.147 / Chapter 6.2 --- Numerical results --- p.154 / Chapter 6.3 --- Discussions --- p.173 / Chapter 7 --- The uniqueness theorem of QNM's --- p.179 / Chapter 7.1 --- A brief review --- p.179 / Chapter 7.2 --- Physical meanings of the conditions --- p.184 / Chapter 7.3 --- The uniqueness theorem of QNM's --- p.188 / Chapter 7.4 --- The generalization of diagonalization --- p.190 / Chapter 7.5 --- Derivation of Green's function method --- p.192 / Chapter 7.6 --- Numerical examples --- p.193 / Chapter 8 --- Conclusion --- p.204 / Chapter A --- The scalar wave equations --- p.207 / Chapter B --- The electromagnetic fields --- p.214 / Chapter C --- Second order expansion in B --- p.217 / Chapter D --- The derivation of D(w) --- p.220 / Chapter E --- The stability of eigenvectors --- p.223

by Tam Chi Yung. / Thesis (M.Phil.)--Chinese University of Hong Kong, 1996. / Includes bibliographical references (leaves 66-67). / by Tam Chi Yung. / Contents --- p.i / List of Figures --- p.iii / Acknowledgement --- p.iv / Abstract --- p.v / Chapter Chapter 1. --- Introduction --- p.1 / Chapter 1.1 --- Open systems and quasinormal modes --- p.1 / Chapter 1.2 --- Gravitational waves --- p.3 / Chapter Chapter 2. --- Green's Function Formalism --- p.6 / Chapter 2.1 --- Introduction --- p.6 / Chapter 2.2 --- Constructing the Green's function --- p.7 / Chapter 2.3 --- The norm --- p.9 / Chapter 2.4 --- Completeness --- p.11 / Chapter Chapter 3. --- Potentials With No Tail --- p.13 / Chapter 3.1 --- Introduction --- p.13 / Chapter 3.2 --- Completeness --- p.14 / Chapter 3.2.1 --- Proof --- p.14 / Chapter 3.2.2 --- Examples --- p.16 / Chapter 3.3 --- The two-component approach --- p.20 / Chapter 3.3.1 --- Formalism --- p.21 / Chapter 3.3.2 --- Comparison of different expansion schemes --- p.23 / Chapter 3.3.3 --- Linear Space --- p.29 / Chapter 3.4 --- Perturbation theory --- p.31 / Chapter 3.4.1 --- Formalism --- p.31 / Chapter 3.4.2 --- Examples --- p.33 / Chapter 3.5 --- Conclusion --- p.35 / Chapter Chapter 4. --- Potentials With Exponential Tails --- p.36 / Chapter 4.1 --- Introduction --- p.36 / Chapter 4.2 --- Single exponential tail --- p.37 / Chapter 4.3 --- Asymptotics of QNM's --- p.40 / Chapter 4.4 --- The Born series --- p.43 / Chapter 4.5 --- Poschl-Teller potential --- p.44 / Chapter 4.5.1 --- Analytic solutions --- p.44 / Chapter 4.5.2 --- The norm --- p.46 / Chapter 4.6 --- The problem of cut-off --- p.48 / Chapter 4.7 --- An effective numerical scheme --- p.49 / Chapter 4.8 --- Conclusion --- p.53 / Chapter Chapter 5. --- Logarithmic Perturbation --- p.54 / Chapter 5.1 --- Introduction --- p.54 / Chapter 5.2 --- Formalism --- p.54 / Chapter 5.3 --- Examples --- p.57 / Chapter 5.4 --- Conclusion --- p.59 / Chapter Chapter 6. --- Conclusion --- p.60 / Appendix A. Asymptotic behaviour of the Green's function --- p.61 / Appendix B. Derivation of the equation (4.16) --- p.63 / Appendix C. Different definitions of the norm --- p.64 / Bibliography --- p.66

Not available / text

We study the role of correlations with the environment as the source of non-Markovian quantum evolutions. We first focus on the impact that correlations with the environment can have on the dynamical map that evolve the system. We expand the set of initial states of a system and its environment that are known to guarantee completely positive reduced dynamics for the system when the combined state evolves unitarily. We characterize the correlations in the initial state in terms of its quantum discord. The induced maps can be not completely positive when quantum correlations including, but not limited to, entanglement are present. We discuss the implications and limitations of the Markov approximation necessary to derive the Kossakowski-Lindblad master equation. A generalized non-Markovian master equation is derived from the dynamical map of systems correlated with their environment. The physical meaning of not completely positive maps is studied to obtain a consistent theory of non-Markovian quantum dynamics. These are associated to inverse maps necessary to establish correlations and they give rise to a canonical embedding map that is local in time. This master equation goes beyond the Kossakowski-Lindblad master equation. Non-equilibrium quantum thermodynamics can be be studied within this theory. Through out this discussion, the general dynamics of two interacting qubits is used as an example for illustrations. / text

Thesis (Ph. D.)--University of Texas at Austin, 2008. / Vita. Includes bibliographical references.

Thesis (Ph. D.)--University of Texas at Austin, 2005. / Supervisor: E. C. George Sudarshan. Vita. Includes bibliographical references.

published_or_final_version / abstract / Chemistry / Doctoral / Doctor of Philosophy

No description available.

No description available.