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

Mark V. Daly-1994-01-01-Arrow@dit (Dublin Institute of Technology)
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TL;DRAbstract

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,
\nis 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
\nconsiderable but, with some necessaxy numerical considerations, we have used it to generate

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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,
\nis 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
\nconsiderable but, with some necessaxy numerical considerations, we have used it to generate

Keywords

Phase spaceQuantumHarmonic oscillatorPhysicsQuantum chaosQuantum systemEigenfunctionWave function

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