April 25, 2001
Thesis Committee: Stephen Teitsworth, Henry Greenside, Joshua Socolar
This thesis examines the dynamical behavior of a vibrating thin metal plate that has the shape of a stadium. This wave system has a corresponding classical system whose shape is chaotic. Having a chaotic shape implies a sensitive dependence on the initial conditions of the system. Thus, if one follows the trajectories of a classical particle confined to a chaotic shape when initialized from nearby points in similar directions, the paths will quickly diverge as the number of reflections increases. However, if the same test is performed with a non-chaotic shape, then the two trajectories will coincide closely for an infinite number of reflections.
The wave equation for the dynamical behavior of our vibrating metal plate can be reduced to a form that corresponds to the equation of motion, or Schrodinger equation, for a quantum point particle in a potential well. Thus, we use our wave system whose corresponding classical system is chaotic to model the behavior of a quantum point particle confined to a stadium-shaped infinite potential well.
The purpose of this research is ultimately to observe effects related to a concept called Quantum Chaos. This term deals with the applicability of a chaotic classical dynamics for the description of a quantum system that exists in what is called the crossover regime. This regime represents the region of transition between the classical and quantum regimes where both interpretations are relevant. A system that exists in this crossover regime exhibits certain unusual properties called scarring, which are of particular interest to this study.
Here is the thesis in PDF: Thesis.pdf (about 5.1 MBytes)