Yuen Pui-Ho. / Thesis (M.Phil.)--Chinese University of Hong Kong, 2002. / Includes bibliographical references (leaves 158-159). / Text in English; abstracts in English and Chinese. / Yuen Pui-Ho. / ACKNOWLEDGEMENTS --- p.1 / ABSTRACT --- p.2 / CONTENTS --- p.4 / LIST OF FIGURES --- p.7 / Chapter CHAPTER 1 - --- INTRODUCTION --- p.13 / Chapter 1-1 --- Interaction with EM-field --- p.15 / Chapter 1-2 --- Objective of this study --- p.17 / Chapter 1-3 --- Thesis arrangement --- p.18 / Chapter CHAPTER 2 - --- LITERATURE REVIEW --- p.20 / Chapter 2-1 --- Numerical Method --- p.20 / Chapter 2-1-1 --- Classical calculation --- p.20 / Chapter 2-1-2 --- Quantum mechanical calculation --- p.21 / Chapter 2-1-2-1 --- Finite Difference Method --- p.21 / Chapter 2-1-2-2 --- Non-finite difference method --- p.23 / Chapter 2-1-3 --- Calculation of dissociation probability --- p.24 / Chapter 2-2 --- Morse oscillator under constant driving frequency --- p.26 / Chapter 2-2-1 --- Classical and quantum dynamics comparison --- p.26 / Chapter 2-2-2 --- Resonance condition and factors affecting dissociation probability --- p.27 / Chapter 2-3 --- MORSE OSCILLATOR UNDER CHIRPED DRIVING FREQUENCY --- p.33 / Chapter 2-3-1 --- Bucket Dynamics --- p.35 / Chapter 2-3-2 --- Floquet Analysis --- p.38 / Chapter 2-4 --- Summaries --- p.43 / Chapter CHAPTER 3 - --- METHODOLOGY --- p.46 / Chapter 3-1 --- The model --- p.46 / Chapter 3-2 --- An approximation to sinusoidal variation --- p.47 / Chapter 3-3 --- Approximation to chirping frequency --- p.51 / Chapter 3-4 --- Calculating time evolution operator for piecewise constant --- p.56 / Chapter 3-5 --- Performance of the piecewise constant approach --- p.58 / Chapter 3-5-1 --- Error vs. time --- p.59 / Chapter 3-5-2 --- Accuracy dependence on number of term included --- p.62 / Chapter 3-5-3 --- Accuracy dependence on applied E-field --- p.64 / Chapter 3-5-4 --- "Drawbacks of the "" piecewise constant approach ´ح" --- p.65 / Chapter CHAPTER 4 - --- BEHAVIOR OF MORSE OSCILLATOR UNDER SEMI-CLASSICAL EM- FIELD --- p.67 / Chapter 4-1 --- Morse oscillator in monochromatic laser light --- p.67 / Chapter 4-1-1 --- Theoretical analysis --- p.67 / Chapter 4-1-2 --- Numerical simulation --- p.70 / Chapter 4-1-2-1 --- Dependence on resonant levels --- p.70 / Chapter 4-1-2-2 --- Dependence on Intensity --- p.76 / Chapter 4-1-2-3 --- Frequency deviation from resonant frequency --- p.79 / Chapter 4-2 --- Morse oscillator driven by chirped laser pulse --- p.89 / Chapter 4-2-1 --- Chirping scheme --- p.89 / Chapter 4-2-2 --- Level climbing and residual --- p.92 / Chapter 4-2-3 --- Factors affecting dissociation probability --- p.98 / Chapter 4-2-3-1 --- Dependence on driving amplitude --- p.98 / Chapter 4-2-3-2 --- Dependence on rate of frequency change and initial driving frequency --- p.99 / Chapter 4-2-3-3 --- Dependency on starting state --- p.104 / Chapter 4-3 --- Chapter Summary --- p.106 / Chapter CHAPTER 5 - --- "BUCKET DYNAMICS AND QUANTUM MECHANICAL ""PHASE SPACE""" --- p.108 / Chapter 5-1 --- Bucket dynamics in classical Morse oscillator --- p.109 / Chapter 5-2 --- "Quantum mechanical ""phase space""" --- p.114 / Chapter 5-2-1 --- Wigner function and its properties --- p.115 / Chapter 5-2-2 --- Q-function and its properties --- p.121 / Chapter 5-2-3 --- Q-functions of the energy eigenstates of Morse oscillator --- p.123 / Chapter 5-3 --- Evolution of Wigner function and Q-function --- p.125 / Chapter 5-3-1 --- Evolution of Wigner function and Q-function under periodic driving field --- p.125 / Chapter 5-3-2 --- Evolution of Wigner function and Q-function under driving field with chirped frequency --- p.132 / Chapter 5-4 --- "Bucket dynamics and, quantum mechanical ""phase space""" --- p.138 / Chapter 5-5 --- Chapter Summary --- p.141 / Chapter CHAPTER 6 - --- CONCLUSIONS AND FURTHER STUDIES --- p.143 / Chapter 6-1 --- Morse oscillator driven by monochromic laser light --- p.143 / Chapter 6-1-1 --- Factors affecting the behavior of Morse oscillator in monochromic laser light --- p.144 / Chapter 6-1-1-1 --- Effect of laser intensity --- p.144 / Chapter 6-1-1-2 --- Effect of driving frequency --- p.144 / Chapter 6-2 --- Morse oscillator driven by chirped laser pulse --- p.145 / Chapter 6-3 --- "Bucket dynamics and quantum mechanical ""phase space""" --- p.146 / Chapter 6-4 --- Wigner function and Q-function of driven Morse oscillator --- p.147 / Chapter 6-5 --- Conclusions and Discussions --- p.149 / APPENDIX A - EQUIVALENCE OF QUANTUM SYSTEMS WITH DIFFERENT GAUGES --- p.150 / APPENDIX B - CALCULATION OF TRANSITION MATRIX ELEMENT TMN --- p.152 / "APPENDIX C - CALCULATION OF PERTURBED MATRIX ELEMENTS, H´ةKN" --- p.154 / BIBLIOGRAPHY --- p.158

No description available.

Numerical methods of resonant dynamics with applications to the Galaxy are considered in this thesis. We derive generating functions for first-order perturbation theory and the associated orbital frequencies by matrix calculus. For two action-angle spaces (J,θ) and (i,φ) related by a canonical map I·φ+s, we show that J can be averaged over ergodic orbits φ to provide an estimator of I to within O(|s|²). We provide examples in one and two dimensions and compare the technique to calculations of actions by numerical line integration in Poincaré sections. We then use spectral dynamics and the Laskar frequency map (Laskar, 1993) to identify the dynamically important resonances of the 'flattened' axisymmetric isochrone potential. We simulate resonant capture in a low-order resonance by populating representative tori of a spherical isochrone Hamiltonian and integrating the orbits while adiabatically introducing axisymmetry. We use the averaging technique described above to observe the fraction of orbits captured, and we compare the result to a theoretical prediction. We return to first-order perturbation theory to analyse its strengths and weaknesses, in particular near orbital pericentre, and when one action is significantly smaller than another. We also reproduce the expected pendulum dynamics in the resonant action-angle plane for orbits in our capture simulation. We develop the concept of adaptive dynamics: we vary the initial orbital energy of the particles in the capture simulations and show that resonant and non-resonant orbits can be identified as clusters in the perturbed action plane. For a given Hamiltonian, we use the perturbed frequencies and a linear regression fit in the action plane as diagnostics of a set of model Hamiltonians on a grid in a suitable parameter space. We find we are able to constrain the parameters of a model Hamiltonian by this method. Finally, we reject the null hypothesis that resonant structures in phase space can be found by traditional methods of density estimation.

Thesis (Ph. D.)--University of Wisconsin--Madison, 1970. / Typescript. Vita. eContent provider-neutral record in process. Description based on print version record. Includes bibliographical references.

We investigate a new perturbation technique introduced by E. Frieman to derive a kinetic equation from the equations of the BBGKY hierarchy. The orders of magnitude of the terms in the latter equations are calculated and Frieman's estimate is found incorrect. His derivation of the Landau's equation for a weakly coupled gas actually depends on the existence of the relaxation time rather than the much shorter mean free time as he expected. A physical interpretation of the Grad's theorem and Grad's original proof is given to justify the choice of the molecular chaos, conditions at the initial time. Two examples are given to clarify the applicability of the perturbation method. / Science, Faculty of / Physics and Astronomy, Department of / Graduate

No description available.

This thesis develops a theory for approximate quantum time-correlation functions, Matsubara dynamics, that rigorously describes how to combine quantum statistics with classical dynamics. Matsubara dynamics is based on Feynman's path integral formulation of quantum mechanics and is expected to describe the physics of any system that satisfies quantum Boltzmann statistics and exhibits rapid quantum decoherence, e.g. liquid water at room temperature. Having derived the Matsubara dynamics theory and explored the symmetry properties that it shares with the quantum Kubo time-correlation function, we demonstrate that two heuristic computational methods, Centroid Molecular Dynamics and Ring Polymer Molecular Dynamics, are based on quantifiable approximations to the Matsubara dynamics time-correlation function. This provides these methods with a stronger theoretical foundation and helps to explain their strengths and shortcomings. We then apply the Matsubara dynamics theory to a recently developed computational method of Poulsen et al. called the planetary model. We show that the planetary model is based on a harmonic approximation to Matsubara dynamics that is engineered to maintain the conservation of the quantum Boltzmann distribution, so quantum statistics and classical dynamics remain harmonised. By making practical modifications to the planetary model, we were able to calculate infrared absorption spectra for a point charge model of condensed-phase water over a range of thermodynamic conditions. We find that this harmonic approximation to Matsubara dynamics provides a good description of bending and vibrational motions and is expected to be a useful tool for future spectroscopic studies of more complex, polarisable models of water.

Thesis (Ph. D.)--University of Texas at Austin, 2000. / Vita. Includes bibliographical references (leaves 62-68). Available also in a digital version from Dissertation Abstracts.

No description available.

Thesis (Ph. D.)--University of Wisconsin--Madison, 1966. / Typescript. Vita. Appendix: "Perturbation treatment of the ground state of H₂⁺" [by] William D. Lyon ... [et al.]: p. 115-120. eContent provider-neutral record in process. Description based on print version record. Includes bibliographical references.