Abstract
dc:descriptionThe quantum kicked rotor has served as a model for testing the ideas of quantum chaos since the field's inception. In this thesis we present an overview of the kicked rotor, both from a semiclassical standpoint as well as from a purely quantum standpoint. At the heart of our kicked rotor model is a generalization of previously considered boundary conditions, corresponding to the presence of a magnetic field. We show that in order for a semiclassical wavefunction of the form e^i/h*S(q) to exist, S(q) must satisfy an iterative version of the classical Hamilton-Jacobi equation. From the purely quantum perspective, the new boundary conditions lead to irrational momentum eigenvalues and a new eigenvalue equation governing the evolution of the system. We develop methods for finding and visualizing solutions of this equation, and we show that the choice of boundary conditions radically affects the localization of the system's eigenstates.
Degree
thesis:*- Name thesis:degree_name
- Ph.D.
- Level thesis:degree_level
- Dissertation
- Discipline thesis:degree_discipline
- Physics
- Year dc:date
- 2012
Author and committee
dc:creator, dc:contributor.*- Author dc:creator
-
- Stuller, Michael Alan
- Contributors dc:contributor
-
- Chang, Shau-Jin
Subjects
dc:subject × 2Rights
dc:rights- Statement dc:rights
-
- ©1999 Michael Alan Stuller
- Language dc:language
- en
Identifiers
dc:identifier.*- Identifier
- 4228785
- OAI identifier oai:identifier
- oai:www.ideals.illinois.edu:2142/31240