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Chang, Shau-Jin Stuller, Michael Alan 2012-05-24T20:24:16Z 2012-05-24T20:24:16Z 10000-01-01 1999 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. Submitted by Elizabeth Kent (eckent2@illinois.edu) on 2012-05-24T20:24:16Z No. of bitstreams: 1 1999_Stuller.pdf: 1526508 bytes, checksum: ce802208898edd50c91dae67d3982ae9 (MD5) Made available in DSpace on 2012-05-24T20:24:16Z (GMT). No. of bitstreams: 1 1999_Stuller.pdf: 1526508 bytes, checksum: ce802208898edd50c91dae67d3982ae9 (MD5) Previous issue date: 1999 Item marked as restricted to the 'UIUC Users [automated]' Group (id=2) by Elizabeth Kent (eckent2@illinois.edu) on 2012-05-24T20:24:16Z Item is restricted indefinitely. Restriction data tranferred 2014-07-01T11:10:49-05:00 Original Data Group with Access UIUC Users [automated] Release Date: none Reason: thesis thesis U of I Only 4228785 http://hdl.handle.net/2142/31240 en ©1999 Michael Alan Stuller quantum chaos kicked rotor The Quantum Kicked Rotor Dissertation / Thesis text Physics Physics University of Illinois at Urbana-Champaign Dissertation Ph.D.