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Classical and quantum chaos in a non-linearly kicked harmonic oscillator

Daly, Mark V (1994) Classical and quantum chaos in a non-linearly kicked harmonic oscillator. PhD thesis, Dublin City University.

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Abstract

The work described m this thesis is based on a detailed analysis of the classical and quantum non linear dynamics of a kicked oscillator. This system belongs to a class of kicked physical systems (time dependent Hamiltonians) whose dynamics have universal properties. We begin the analysis by considering the classical mapping (recursive relationship) derived from the parent system equations. The analysis covers the system ’s phase space and its evolution as parameters are changed. The detailed orbit structure is obtained and the break-up of this orbit structure in the phase space, influenced by presence of periodic orbits, is examined thoroughly. We also show the existence of two types of orbital diffusion (normal diffusion and a resonance enhanced diffusion). The results from this classical analysis are then compared with the quantum mapping. The complexity of this quantum mapping is considerable but, with some necessaxy numerical considerations, we have used it to generate the time evolution of the quantum probability amplitudes of the system ’s eigenfunctions. These amplitudes permit the calculation of the system ’s energy as time progresses and enable us to compare the quasi-phase space given by the Wigner distrubution with the classical manifold structure to check for scarring of the quantum wavefunctions. The quantum mapping we denve has not been defined in any of the literature so that all the results obtained in the quantum regime are original. In the classical regime our work on periodic orbits and resonance enhanced diffusion is also original. We have adopted some techniques and methods from other kicked systems and modified them for our system to complete the investigation of the kicked oscillator.

Item Type:Thesis (PhD)
Date of Award:1994
Refereed:No
Supervisor(s):Heffernan, Daniel M.
Uncontrolled Keywords:Chaos theory; Chaotic behaviour; kicked oscialators; Time dependent Hamiltonians
Subjects:Physical Sciences > Physics
Mathematics > Mathematical physics
DCU Faculties and Centres:DCU Faculties and Schools > Faculty of Science and Health > School of Physical Sciences
Use License:This item is licensed under a Creative Commons Attribution-NonCommercial-No Derivative Works 3.0 License. View License
ID Code:18470
Deposited On:19 Jul 2013 11:20 by Celine Campbell. Last Modified 19 Jul 2013 11:20

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