{"id":{"repo_id":"maryland","oai_identifier":"oai:drum.lib.umd.edu:1903/14524"},"canonical_url":"https://search.dev.ndltd.org/etd/maryland/oai:drum.lib.umd.edu:1903/14524","repository":{"repo_id":"maryland","name":"University of Maryland","base_url":"https://api.drum.lib.umd.edu/server/oai/request"},"display":{"title":"Statistical Modeling of Wave Chaotic Transport and Tunneling","abstract":"This thesis treats two general problem areas in the field of wave chaos. The first problem area that we address concerns short wavelength tunneling from a classically confined region in which the classical orbits are chaotic. We de- velop a quantitative theory for the statistics of energy level splittings for symmetric chaotic wells separated by a tunneling barrier. Our theory is based on the ran- dom plane wave hypothesis. While the fluctuation statistics are very different for chaotic and non-chaotic well dynamics, we show that the mean splittings of differ- ently shaped wells, including integrable and chaotic wells, are the same if their well areas and barrier parameters are the same. We also consider the case of tunneling from a single well into a region with outgoing quantum waves. Our second problem area concerns the statistical properties of the impedance matrix (related to the scattering matrix) describing the input/output properties of waves in cavities in which ray trajectories that are regular and chaotic coexist (i.e., `mixed' systems). The impedance can be written as a summation over eigenmodes where the eigenmodes can typically be classified as either regular or chaotic. By appropriate characterizations of regular and chaotic contributions, we obtain statis- tical predictions for the impedance. We then test these predictions by comparison with numerical calculations for a specific cavity shape, obtaining good agreement.","abstract_html":"This thesis treats two general problem areas in the field of wave chaos. The first problem area that we address concerns short wavelength tunneling from a classically confined region in which the classical orbits are chaotic. We de- velop a quantitative theory for the statistics of energy level splittings for symmetric chaotic wells separated by a tunneling barrier. Our theory is based on the ran- dom plane wave hypothesis. While the fluctuation statistics are very different for chaotic and non-chaotic well dynamics, we show that the mean splittings of differ- ently shaped wells, including integrable and chaotic wells, are the same if their well areas and barrier parameters are the same. We also consider the case of tunneling from a single well into a region with outgoing quantum waves. Our second problem area concerns the statistical properties of the impedance matrix (related to the scattering matrix) describing the input/output properties of waves in cavities in which ray trajectories that are regular and chaotic coexist (i.e., `mixed' systems). The impedance can be written as a summation over eigenmodes where the eigenmodes can typically be classified as either regular or chaotic. By appropriate characterizations of regular and chaotic contributions, we obtain statis- tical predictions for the impedance. We then test these predictions by comparison with numerical calculations for a specific cavity shape, obtaining good agreement.","abstract_has_math":false,"creators":["Lee, Ming-Jer"],"institution":null,"degree_name":null,"degree_level":null,"degree_discipline":null,"degree_department":"Physics","school":null,"contributors":[],"advisors":["Ott, Edward"],"committee_chairs":[],"committee_members":[],"year":2013,"date_issued":"2013","date_published":"2013","updated_at":"2026-07-24T03:02:18Z","subjects":[],"languages":[],"rights":[],"rights_urls":[],"identifier_entries":[]},"links":{"outbound_url":"http://hdl.handle.net/1903/14524","outbound_label":"Handle","outbound_source":"dc:identifier.uri"},"metadata_groups":[{"id":"people","label":"People","entries":[{"key":"dc:contributor.advisor","label":"Advisor","values":["Ott, Edward"]},{"key":"dc:contributor.department","label":"Department","values":["Physics"]},{"key":"dc:creator","label":"Author","values":["Lee, Ming-Jer"]}]},{"id":"academic_context","label":"Academic Context","entries":[{"key":"dc:date.accessioned","label":"Dc Date Accessioned","values":["2013-10-04T05:30:55Z"]},{"key":"dc:date.available","label":"Dc Date Available","values":["2013-10-04T05:30:55Z"]},{"key":"dc:date.issued","label":"Date","values":["2013"]},{"key":"dc:type","label":"Dc Type","values":["Dissertation"]}]},{"id":"identifiers","label":"Identifiers","entries":[{"key":"dc:identifier.uri","label":"Identifier URI","values":["http://hdl.handle.net/1903/14524"]}]},{"id":"additional","label":"Additional Metadata","entries":[{"key":"dc:description.abstract","label":"Abstract","values":["This thesis treats two general problem areas in the field of wave chaos. The first problem area that we address concerns short wavelength tunneling from a classically confined region in which the classical orbits are chaotic. We de- velop a quantitative theory for the statistics of energy level splittings for symmetric chaotic wells separated by a tunneling barrier. Our theory is based on the ran- dom plane wave hypothesis. While the fluctuation statistics are very different for chaotic and non-chaotic well dynamics, we show that the mean splittings of differ- ently shaped wells, including integrable and chaotic wells, are the same if their well areas and barrier parameters are the same. We also consider the case of tunneling from a single well into a region with outgoing quantum waves. Our second problem area concerns the statistical properties of the impedance matrix (related to the scattering matrix) describing the input/output properties of waves in cavities in which ray trajectories that are regular and chaotic coexist (i.e., `mixed' systems). The impedance can be written as a summation over eigenmodes where the eigenmodes can typically be classified as either regular or chaotic. By appropriate characterizations of regular and chaotic contributions, we obtain statis- tical predictions for the impedance. We then test these predictions by comparison with numerical calculations for a specific cavity shape, obtaining good agreement."]},{"key":"dc:title","label":"Title","values":["Statistical Modeling of Wave Chaotic Transport and Tunneling"]}]}],"canonical_facts":{"dc:contributor.advisor":["Ott, Edward"],"dc:contributor.department":["Physics"],"dc:creator":["Lee, Ming-Jer"],"dc:date.accessioned":["2013-10-04T05:30:55Z"],"dc:date.available":["2013-10-04T05:30:55Z"],"dc:date.issued":["2013"],"dc:description.abstract":["This thesis treats two general problem areas in the field of wave chaos. The first problem area that we address concerns short wavelength tunneling from a classically confined region in which the classical orbits are chaotic. We de- velop a quantitative theory for the statistics of energy level splittings for symmetric chaotic wells separated by a tunneling barrier. Our theory is based on the ran- dom plane wave hypothesis. While the fluctuation statistics are very different for chaotic and non-chaotic well dynamics, we show that the mean splittings of differ- ently shaped wells, including integrable and chaotic wells, are the same if their well areas and barrier parameters are the same. We also consider the case of tunneling from a single well into a region with outgoing quantum waves. Our second problem area concerns the statistical properties of the impedance matrix (related to the scattering matrix) describing the input/output properties of waves in cavities in which ray trajectories that are regular and chaotic coexist (i.e., `mixed' systems). The impedance can be written as a summation over eigenmodes where the eigenmodes can typically be classified as either regular or chaotic. By appropriate characterizations of regular and chaotic contributions, we obtain statis- tical predictions for the impedance. We then test these predictions by comparison with numerical calculations for a specific cavity shape, obtaining good agreement."],"dc:identifier.uri":["http://hdl.handle.net/1903/14524"],"dc:title":["Statistical Modeling of Wave Chaotic Transport and Tunneling"],"dc:type":["Dissertation"]},"updated_at":"2026-07-24T03:02:18Z"}