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Dissertation
Chaotic scattering on attractive potentials
Doctor of Philosophy (Ph.D.), Drexel University
May 1998
DOI:
https://doi.org/10.17918/00000643
Abstract
This thesis investigates chaotic scattering in two distinct Hamiltonian systems. The classical scattering of a particle in two dimensions on a billiard shape potential is studied. An investigation of the dynamics of the bound map for a billiard with a quadrupole deformation is presented. The scattering dynamics resulting for positive energies for this billiard is analyzed in light of the bound dynamics. Symmetry lines of the map are used to find the relevant periodic orbits. The manifolds that are most influential on the scattering behavior are identified. Strong focusing effects are found in the scattering functions. The existence of these preferred scattering directions is shown to be a consequence of large scale features of the phase space such as the period-two orbits. Self-similarity is directly linked to unstable periodic orbits of the bound phase space. The main observations and methodology are applicable to concave billiards in general. The classical and quantum chaotic scattering of a particle on a smooth two-well potential is also investigated. A symbolic dynamical representation is found that characterizes the momentum-impact parameter space. The quantum mechanical solution of the two well system is obtained. A formal derivation of the integral equations is presented, the "S-matrix" is defined. A numerical algorithm for solving the integral equations is developed and implemented. The limitations of the method for studying this system in the semi-classical regime are analyzed. The statistics of the resulting S-matrices are compared with the predictions of Random Matrix Theory for circular orthogonal ensembles.
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Details
- Title
- Chaotic scattering on attractive potentials
- Creators
- Vincent James Daniels
- Contributors
- Michel Vallieres (Advisor)
- Awarding Institution
- Drexel University
- Degree Awarded
- Doctor of Philosophy (Ph.D.)
- Publisher
- Drexel University; Philadelphia, Pennsylvania
- Number of pages
- xvii, 210 pages
- Resource Type
- Dissertation
- Language
- English
- Academic Unit
- College of Arts and Sciences; Physics; Drexel University
- Other Identifier
- 991014970215104721