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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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.
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