{"id":{"repo_id":"uiuc","oai_identifier":"oai:www.ideals.illinois.edu:2142/31240"},"canonical_url":"https://search.dev.ndltd.org/etd/uiuc/oai:www.ideals.illinois.edu:2142/31240","repository":{"repo_id":"uiuc","name":"University of Illinois - Urbana-Champaign","base_url":"https://www.ideals.illinois.edu/oai-pmh"},"display":{"title":"The Quantum Kicked Rotor","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.","abstract_html":"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.","abstract_has_math":false,"creators":["Stuller, Michael Alan"],"institution":null,"degree_name":"Ph.D.","degree_level":"Dissertation","degree_discipline":"Physics","degree_department":null,"school":null,"contributors":["Chang, Shau-Jin"],"advisors":[],"committee_chairs":[],"committee_members":[],"year":2012,"date_issued":"2012-05-24T20:24:16Z","date_published":"2012-05-24T20:24:16Z","updated_at":"2026-07-22T22:25:30Z","subjects":["quantum chaos","kicked rotor"],"languages":["en"],"rights":["©1999 Michael Alan Stuller"],"rights_urls":[],"identifier_entries":[{"key":"dc:identifier","label":"Identifier","values":["4228785"],"render_values":[{"text":"4228785","href":null,"code":true}]}]},"links":{"outbound_url":"http://hdl.handle.net/2142/31240","outbound_label":"Handle","outbound_source":"dc:identifier"},"metadata_groups":[{"id":"people","label":"People","entries":[{"key":"dc:contributor","label":"Contributor","values":["Chang, Shau-Jin"]},{"key":"dc:creator","label":"Author","values":["Stuller, Michael Alan"]}]},{"id":"academic_context","label":"Academic Context","entries":[{"key":"dc:date","label":"Dc Date","values":["2012-05-24T20:24:16Z","10000-01-01","1999"]},{"key":"dc:type","label":"Dc Type","values":["Dissertation / Thesis","text"]},{"key":"thesis:degree_discipline","label":"Discipline","values":["Physics"]},{"key":"thesis:degree_level","label":"Degree Level","values":["Dissertation"]},{"key":"thesis:degree_name","label":"Degree Name","values":["Ph.D."]}]},{"id":"subjects_keywords","label":"Subjects and Keywords","entries":[{"key":"dc:subject","label":"Dc Subject","values":["quantum chaos","kicked rotor"]}]},{"id":"language_rights","label":"Language and Rights","entries":[{"key":"dc:language","label":"Dc Language","values":["en"]},{"key":"dc:rights","label":"Dc Rights","values":["©1999 Michael Alan Stuller"]}]},{"id":"identifiers","label":"Identifiers","entries":[{"key":"dc:identifier","label":"Identifier","values":["4228785","http://hdl.handle.net/2142/31240"]}]},{"id":"additional","label":"Additional Metadata","entries":[{"key":"dc:description","label":"Description","values":["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"]},{"key":"dc:title","label":"Title","values":["The Quantum Kicked Rotor"]}]}],"canonical_facts":{"dc:contributor":["Chang, Shau-Jin"],"dc:creator":["Stuller, Michael Alan"],"dc:date":["2012-05-24T20:24:16Z","10000-01-01","1999"],"dc:description":["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"],"dc:identifier":["4228785","http://hdl.handle.net/2142/31240"],"dc:language":["en"],"dc:rights":["©1999 Michael Alan Stuller"],"dc:subject":["quantum chaos","kicked rotor"],"dc:title":["The Quantum Kicked Rotor"],"dc:type":["Dissertation / Thesis","text"],"thesis:degree_discipline":["Physics"],"thesis:degree_level":["Dissertation"],"thesis:degree_name":["Ph.D."]},"updated_at":"2026-07-22T22:25:30Z"}