{"id":{"repo_id":"uiuc","oai_identifier":"oai:www.ideals.illinois.edu:2142/109357"},"canonical_url":"https://search.dev.ndltd.org/etd/uiuc/oai:www.ideals.illinois.edu:2142/109357","repository":{"repo_id":"uiuc","name":"University of Illinois - Urbana-Champaign","base_url":"https://www.ideals.illinois.edu/oai-pmh"},"display":{"title":"Development of potential-based time domain integral equations for quantum electrodynamics modeling","abstract":"Quantum technologies that significantly depend on electromagnetic effects are becoming of increasing interest to engineers. In many important cases, the quantum electrodynamics models that describe these technologies can be solved using information about the electromagnetic environment provided by computational electromagnetics methods operating purely in the classical regime. However, the unique requirements imposed by these applications are stressing the capabilities of traditional computational electromagnetics methods. To address this, time domain integral equation methods formulated directly in terms of the magnetic vector and electric scalar potentials are systematically developed for the analysis of perfectly conducting and penetrable regions. A rigorous functional framework is utilized to analyze the Sobolev space properties of these integral equations. Discretizations formulated to conform to these Sobolev space properties are shown to be substantially more stable numerically than traditional discretization approaches. These new computational electromagnetics methods are then utilized in a novel framework developed to determine the spatially-dependent quantized field operators produced by a single photon source built from a transmon qubit.","abstract_html":"Quantum technologies that significantly depend on electromagnetic effects are becoming of increasing interest to engineers. In many important cases, the quantum electrodynamics models that describe these technologies can be solved using information about the electromagnetic environment provided by computational electromagnetics methods operating purely in the classical regime. However, the unique requirements imposed by these applications are stressing the capabilities of traditional computational electromagnetics methods. To address this, time domain integral equation methods formulated directly in terms of the magnetic vector and electric scalar potentials are systematically developed for the analysis of perfectly conducting and penetrable regions. A rigorous functional framework is utilized to analyze the Sobolev space properties of these integral equations. Discretizations formulated to conform to these Sobolev space properties are shown to be substantially more stable numerically than traditional discretization approaches. These new computational electromagnetics methods are then utilized in a novel framework developed to determine the spatially-dependent quantized field operators produced by a single photon source built from a transmon qubit.","abstract_has_math":false,"creators":["Roth, Thomas E"],"institution":"University of Illinois at Urbana-Champaign","degree_name":"Ph.D.","degree_level":"Dissertation","degree_discipline":"Electrical & Computer Engr","degree_department":null,"school":null,"contributors":["Chew, Weng C","Leburton, Jean-Pierre","Popescu, Gabriel","Peng, Zhen"],"advisors":[],"committee_chairs":[],"committee_members":[],"year":2021,"date_issued":"2021-03-05T21:36:56Z","date_published":"2021-03-05T21:36:56Z","updated_at":"2026-07-22T22:24:50Z","subjects":["Computational electromagnetics","time domain integral equations","quantum electrodynamics"],"languages":["en"],"rights":["Copyright 2020 Thomas E. 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To address this, time domain integral equation methods formulated directly in terms of the magnetic vector and electric scalar potentials are systematically developed for the analysis of perfectly conducting and penetrable regions. A rigorous functional framework is utilized to analyze the Sobolev space properties of these integral equations. Discretizations formulated to conform to these Sobolev space properties are shown to be substantially more stable numerically than traditional discretization approaches. These new computational electromagnetics methods are then utilized in a novel framework developed to determine the spatially-dependent quantized field operators produced by a single photon source built from a transmon qubit.","Submission original under an indefinite embargo labeled 'Open Access'. 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In many important cases, the quantum electrodynamics models that describe these technologies can be solved using information about the electromagnetic environment provided by computational electromagnetics methods operating purely in the classical regime. However, the unique requirements imposed by these applications are stressing the capabilities of traditional computational electromagnetics methods. To address this, time domain integral equation methods formulated directly in terms of the magnetic vector and electric scalar potentials are systematically developed for the analysis of perfectly conducting and penetrable regions. A rigorous functional framework is utilized to analyze the Sobolev space properties of these integral equations. Discretizations formulated to conform to these Sobolev space properties are shown to be substantially more stable numerically than traditional discretization approaches. These new computational electromagnetics methods are then utilized in a novel framework developed to determine the spatially-dependent quantized field operators produced by a single photon source built from a transmon qubit.","Submission original under an indefinite embargo labeled 'Open Access'. The submission was exported from vireo on 2021-03-04 without embargo terms","The student, Thomas Roth, accepted the attached license on 2020-11-11 at 14:13.","The student, Thomas Roth, submitted this Dissertation for approval on 2020-11-11 at 14:21.","This Dissertation was approved for publication on 2020-11-12 at 16:40.","DSpace SAF Submission Ingestion Package generated from Vireo submission #15874 on 2021-03-04 at 15:34:25","Made available in DSpace on 2021-03-05T21:36:56Z (GMT). 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