{"id":{"repo_id":"uiuc","oai_identifier":"oai:www.ideals.illinois.edu:2142/31305"},"canonical_url":"https://search.dev.ndltd.org/etd/uiuc/oai:www.ideals.illinois.edu:2142/31305","repository":{"repo_id":"uiuc","name":"University of Illinois - Urbana-Champaign","base_url":"https://www.ideals.illinois.edu/oai-pmh"},"display":{"title":"Semiclassical approaches to Quantal Andreev Billiards and Other Topics in Inhomogeneous Superconductivity","abstract":"Semiclassical approaches to inhomogeneous superconductivity are explored within three settings. The first is that of Andreev billiards, which are finite, arbitrarily-shaped, normal-state regions, surrounded by superconductor. A theoretical framework for the investigation of the short-wave quantal properties of quasiparticles in Andreev billiards is developed. Among the central results are two semiclassical trace formulas for the density of states. The first, a lower-resolution formula, corresponds to the well-known quasiclassical approximation. The second, a higher-resolution formula, allows the density of states to be expressed in terms of: (i) An explicit formula, valid in the short-wave limit, for billiards of arbitrary shape and dimensionality; and (ii) Higher-resolution corrections, expressed as a sum over periodic orbits that creep around the billiard boundary. The second involves quasiparticle motion near an extended impurity in a d-wave superconductor. Via an extension of the quasiclassical approximation, the idea that sign-variations in the superconducting pair-potential lead to low-energy states is extended beyond its original setting of boundary scattering to the broader context of scattering by general single-particle potentials. The index-theoretic origin of these states is exhibited via a connection with Witten's super-symmetric quantum-mechanical model. The third concerns an extended impurity in a cuprate superconductor in the pseudogap regime. It is shown that if the d-wave correlations persist into the pseudogap regime, but with pair-potential phase-fluctuations that destroy long-range ordering, then the low-energy states near extended impurities in the superconducting state should persist as resonances in the pseudogap regime. Thus, such states can serve as a probe of d-wave correlations in the pseudogap regime.","abstract_html":"Semiclassical approaches to inhomogeneous superconductivity are explored within three settings. The first is that of Andreev billiards, which are finite, arbitrarily-shaped, normal-state regions, surrounded by superconductor. A theoretical framework for the investigation of the short-wave quantal properties of quasiparticles in Andreev billiards is developed. Among the central results are two semiclassical trace formulas for the density of states. The first, a lower-resolution formula, corresponds to the well-known quasiclassical approximation. The second, a higher-resolution formula, allows the density of states to be expressed in terms of: (i) An explicit formula, valid in the short-wave limit, for billiards of arbitrary shape and dimensionality; and (ii) Higher-resolution corrections, expressed as a sum over periodic orbits that creep around the billiard boundary. The second involves quasiparticle motion near an extended impurity in a d-wave superconductor. Via an extension of the quasiclassical approximation, the idea that sign-variations in the superconducting pair-potential lead to low-energy states is extended beyond its original setting of boundary scattering to the broader context of scattering by general single-particle potentials. The index-theoretic origin of these states is exhibited via a connection with Witten's super-symmetric quantum-mechanical model. The third concerns an extended impurity in a cuprate superconductor in the pseudogap regime. It is shown that if the d-wave correlations persist into the pseudogap regime, but with pair-potential phase-fluctuations that destroy long-range ordering, then the low-energy states near extended impurities in the superconducting state should persist as resonances in the pseudogap regime. Thus, such states can serve as a probe of d-wave correlations in the pseudogap regime.","abstract_has_math":false,"creators":["Adagideli, İnanc̜"],"institution":null,"degree_name":"Ph.D.","degree_level":"Dissertation","degree_discipline":"Physics","degree_department":null,"school":null,"contributors":["Goldbart, Paul M."],"advisors":[],"committee_chairs":[],"committee_members":[],"year":2012,"date_issued":"2012-05-31T15:56:02Z","date_published":"2012-05-31T15:56:02Z","updated_at":"2026-07-22T22:25:30Z","subjects":["inhomogeneous superconductor","Andreev billiards","cuprate superconductors"],"languages":["en"],"rights":["©2001 İnanc̜ Adagideli"],"rights_urls":[],"identifier_entries":[{"key":"dc:identifier","label":"Identifier","values":["4549671"],"render_values":[{"text":"4549671","href":null,"code":true}]}]},"links":{"outbound_url":"http://hdl.handle.net/2142/31305","outbound_label":"Handle","outbound_source":"dc:identifier"},"metadata_groups":[{"id":"people","label":"People","entries":[{"key":"dc:contributor","label":"Contributor","values":["Goldbart, Paul M."]},{"key":"dc:creator","label":"Author","values":["Adagideli, İnanc̜"]}]},{"id":"academic_context","label":"Academic Context","entries":[{"key":"dc:date","label":"Dc Date","values":["2012-05-31T15:56:02Z","10000-01-01","2001"]},{"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":["inhomogeneous superconductor","Andreev billiards","cuprate superconductors"]}]},{"id":"language_rights","label":"Language and Rights","entries":[{"key":"dc:language","label":"Dc Language","values":["en"]},{"key":"dc:rights","label":"Dc Rights","values":["©2001 İnanc̜ Adagideli"]}]},{"id":"identifiers","label":"Identifiers","entries":[{"key":"dc:identifier","label":"Identifier","values":["4549671","http://hdl.handle.net/2142/31305"]}]},{"id":"additional","label":"Additional Metadata","entries":[{"key":"dc:description","label":"Description","values":["Semiclassical approaches to inhomogeneous superconductivity are explored within three settings. The first is that of Andreev billiards, which are finite, arbitrarily-shaped, normal-state regions, surrounded by superconductor. A theoretical framework for the investigation of the short-wave quantal properties of quasiparticles in Andreev billiards is developed. Among the central results are two semiclassical trace formulas for the density of states. The first, a lower-resolution formula, corresponds to the well-known quasiclassical approximation. The second, a higher-resolution formula, allows the density of states to be expressed in terms of: (i) An explicit formula, valid in the short-wave limit, for billiards of arbitrary shape and dimensionality; and (ii) Higher-resolution corrections, expressed as a sum over periodic orbits that creep around the billiard boundary. The second involves quasiparticle motion near an extended impurity in a d-wave superconductor. Via an extension of the quasiclassical approximation, the idea that sign-variations in the superconducting pair-potential lead to low-energy states is extended beyond its original setting of boundary scattering to the broader context of scattering by general single-particle potentials. The index-theoretic origin of these states is exhibited via a connection with Witten's super-symmetric quantum-mechanical model. The third concerns an extended impurity in a cuprate superconductor in the pseudogap regime. It is shown that if the d-wave correlations persist into the pseudogap regime, but with pair-potential phase-fluctuations that destroy long-range ordering, then the low-energy states near extended impurities in the superconducting state should persist as resonances in the pseudogap regime. Thus, such states can serve as a probe of d-wave correlations in the pseudogap regime.","Submitted by Elizabeth Kent (eckent2@illinois.edu) on 2012-05-31T15:56:02Z No. of bitstreams: 1 2001_adagideli.pdf: 5312117 bytes, checksum: 256af3412c30b16ff104debe58a62c7a (MD5)","Made available in DSpace on 2012-05-31T15:56:02Z (GMT). No. of bitstreams: 1 2001_adagideli.pdf: 5312117 bytes, checksum: 256af3412c30b16ff104debe58a62c7a (MD5) Previous issue date: 2001","Restriction data tranferred 2014-07-01T11:10:50-05:00 Original Data Group with Access UIUC Users [automated] Release Date: none Reason: thesis","Item marked as restricted to the 'UIUC Users [automated]' Group (id=2) by Elizabeth Kent (eckent2@illinois.edu) on 2012-05-31T15:56:02Z Item is restricted indefinitely.","thesis","U of I Only"]},{"key":"dc:title","label":"Title","values":["Semiclassical approaches to Quantal Andreev Billiards and Other Topics in Inhomogeneous Superconductivity"]}]}],"canonical_facts":{"dc:contributor":["Goldbart, Paul M."],"dc:creator":["Adagideli, İnanc̜"],"dc:date":["2012-05-31T15:56:02Z","10000-01-01","2001"],"dc:description":["Semiclassical approaches to inhomogeneous superconductivity are explored within three settings. The first is that of Andreev billiards, which are finite, arbitrarily-shaped, normal-state regions, surrounded by superconductor. A theoretical framework for the investigation of the short-wave quantal properties of quasiparticles in Andreev billiards is developed. Among the central results are two semiclassical trace formulas for the density of states. The first, a lower-resolution formula, corresponds to the well-known quasiclassical approximation. The second, a higher-resolution formula, allows the density of states to be expressed in terms of: (i) An explicit formula, valid in the short-wave limit, for billiards of arbitrary shape and dimensionality; and (ii) Higher-resolution corrections, expressed as a sum over periodic orbits that creep around the billiard boundary. The second involves quasiparticle motion near an extended impurity in a d-wave superconductor. Via an extension of the quasiclassical approximation, the idea that sign-variations in the superconducting pair-potential lead to low-energy states is extended beyond its original setting of boundary scattering to the broader context of scattering by general single-particle potentials. The index-theoretic origin of these states is exhibited via a connection with Witten's super-symmetric quantum-mechanical model. The third concerns an extended impurity in a cuprate superconductor in the pseudogap regime. It is shown that if the d-wave correlations persist into the pseudogap regime, but with pair-potential phase-fluctuations that destroy long-range ordering, then the low-energy states near extended impurities in the superconducting state should persist as resonances in the pseudogap regime. Thus, such states can serve as a probe of d-wave correlations in the pseudogap regime.","Submitted by Elizabeth Kent (eckent2@illinois.edu) on 2012-05-31T15:56:02Z No. of bitstreams: 1 2001_adagideli.pdf: 5312117 bytes, checksum: 256af3412c30b16ff104debe58a62c7a (MD5)","Made available in DSpace on 2012-05-31T15:56:02Z (GMT). No. of bitstreams: 1 2001_adagideli.pdf: 5312117 bytes, checksum: 256af3412c30b16ff104debe58a62c7a (MD5) Previous issue date: 2001","Restriction data tranferred 2014-07-01T11:10:50-05:00 Original Data Group with Access UIUC Users [automated] Release Date: none Reason: thesis","Item marked as restricted to the 'UIUC Users [automated]' Group (id=2) by Elizabeth Kent (eckent2@illinois.edu) on 2012-05-31T15:56:02Z Item is restricted indefinitely.","thesis","U of I Only"],"dc:identifier":["4549671","http://hdl.handle.net/2142/31305"],"dc:language":["en"],"dc:rights":["©2001 İnanc̜ Adagideli"],"dc:subject":["inhomogeneous superconductor","Andreev billiards","cuprate superconductors"],"dc:title":["Semiclassical approaches to Quantal Andreev Billiards and Other Topics in Inhomogeneous Superconductivity"],"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"}