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https://hdl.handle.net/2142/31240
Description
Title
The Quantum Kicked Rotor
Author(s)
Stuller, Michael Alan
Issue Date
1999
Doctoral Committee Chair(s)
Chang, Shau-Jin
Department of Study
Physics
Discipline
Physics
Degree Name
Ph.D.
Degree Level
Dissertation
Keyword(s)
quantum chaos
kicked rotor
Language
en
Abstract
The 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.
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