by Law Chi Kwong. / Parallel title in Chinese characters. / Thesis (M.Phil.)--Chinese University of Hong Kong, 1989. / Bibliography: leaves 73-75. / by Law Chi Kwong.

Chan Chung Ning. / Thesis (M.Phil.)--Chinese University of Hong Kong, 1999. / Includes bibliographical references (leaves [86]-88). / Text in English; abstracts in English and Chinese. / Chan Chung Ning. / Abstract --- p.i / Abstract in Chinese --- p.ii / Acknowledgement --- p.iii / Contents --- p.iv / List of Figures --- p.vii / List of Tables --- p.xi / Chapter Chapter 1. --- Introduction --- p.1 / Chapter 1.1 --- Classical chaos and quantum chaos --- p.1 / Chapter 1.2 --- Motivations --- p.2 / Chapter 1.3 --- Structure of our study --- p.3 / Chapter Chapter 2. --- Integrability of Hamiltonian Systems --- p.5 / Chapter 2.1 --- Integrable systems --- p.5 / Chapter 2.2 --- KAM perturbation and Poincare surface section --- p.8 / Chapter 2.3 --- Surface sections of Robnik Billiards --- p.11 / Chapter 2.4 --- Linking classical and quantum chaos --- p.16 / Chapter Chapter 3. --- Constraint Operator Method --- p.18 / Chapter 3.1 --- Two-dimensional billiards --- p.18 / Chapter 3.2 --- Formalism of the constraint operator method with the Dirichlet boundary conditions --- p.19 / Chapter 3.3 --- Numerical results: eigenvalues of billiards --- p.24 / Chapter 3.4 --- Discussion on the constraint operator method --- p.29 / Chapter Chapter 4. --- The COM with the Neumann Boundary Conditions --- p.32 / Chapter 4.1 --- Formalism --- p.32 / Chapter 4.2 --- Numerical results --- p.35 / Chapter 4.3 --- Discussion --- p.38 / Chapter Chapter 5. --- Boundary Integral Method --- p.40 / Chapter 5.1 --- Introduction --- p.40 / Chapter 5.2 --- Berry's formalism --- p.41 / Chapter 5.3 --- A modified formalism --- p.46 / Chapter 5.4 --- Numerical results --- p.47 / Chapter 5.5 --- Discussion on the BIM --- p.53 / Chapter Chapter 6. --- Further Discussions on the BIM --- p.55 / Chapter 6.1 --- The choice of the Green's function --- p.55 / Chapter 6.2 --- Principal value --- p.58 / Chapter Chapter 7. --- Conformal Mapping Method --- p.64 / Chapter 7.1 --- Formalism --- p.64 / Chapter 7.2 --- Numerical results --- p.69 / Chapter 7.3 --- Summary --- p.73 / Chapter Chapter 8. --- Spectral Statistics --- p.76 / Chapter 8.1 --- Introduction --- p.76 / Chapter 8.2 --- Numerical results --- p.78 / Chapter 8.3 --- Summary --- p.80 / Chapter Chapter 9. --- Conclusion --- p.83 / Bibliography --- p.86

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A thesis submitted to the Faculty of Science, University of the Witwatersrand, Johannesburg, South Africa, in fulfilment of the requirements for the Degree of Doctor of Philosophy. / Quantum chaos is associated with the phenomenon of avoided level crossings on a large scale which leads to a statistical behaviour similar to that of a Gaussian Orthogonal Ensemble (GOE) of matrices. (Abbreviation abstract) / Andrew Chakane 2019

Thesis (Ph. D.)--University of Texas at Austin, 2001. / Vita. Includes bibliographical references (leaves 179-187). Available also in a digital version from Dissertation Abstracts.

Thesis (Ph. D.)--University of Texas at Austin, 1998. / Vita. Includes bibliographical references (leaves 114-121). Available also in a digital version from Dissertation Abstracts.

The evolution of classically chaotic quantum systems is analyzed within the formalism of Quantum Pseudo-Probability Distributions. Due to the deep connections that a quantum system shows with its classical correspondent in this representation, the Pseudo-Probability formalism appears to be a useful method of investigation in the field of "Quantum Chaos." In the first part of the thesis we generalize this formalism to quantum systems containing spin operators. It is shown that a classical-like equation of motion for the pseudo-probability distribution ρw can be constructed, dρw/dt = (L_CL + L_QGD)ρw, which is rigorously equivalent to the quantum von Neumann-Liouville equation. The operator L_CL is undistinguishable from the classical operator that generates the semiclassical equations of motion. In the case of the spin-boson system this operator produces semiclassical chaos and is responsible for quantum irreversibility and the fast growth of quantum uncertainty. Carrying out explicit calculations for a spin-boson Hamiltonian the joint action of L_CL and L_QGD is illustrated. It is shown that the latter operator, L_QGD makes the spin system 'remember' its quantum nature, and competes with the irreversibility induced by the former operator. In the second part we test the idea of the enhancement of the quantum uncertainty triggered by the classical chaos by investigating the analogous effect of diffusive excitation in periodically kicked quantum systems. The classical correspondents of these quantum systems exhibit, in the chaotic region, diffusive behavior of the unperturbed energy. For the Quantum Kicked Harmonic Oscillator, in the case of quantum resonances, we provide an exact solution of the quantum evolution. This proves the existence of a deterministic drift in the energy increase over time of the system considered. More generally, this "superdiffusive" excitation of the energy is due to coherent quantum mechanical tunnelling between degenerate tori of the classical phase space. In conclusion we find that some of the quantum effects resulting from this fast increase do not have any classical counterpart, they are mainly tunnelling processes. This seems to be the first observation of an effect of this kind.

The quantum dynamics of minimum uncertainty wave packets in a system described by the surface-state-electron (SSE) Hamiltonian are studied herein.

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