Standing wave solutions to the Maxwell–Chern–Simons–Schrödinger equations
We prove the existence of standing wave solutions for the Maxwell–Chern–Simons–Schrödinger equation. This model describes the fractional quantum Hall effect and anyonic superconductivity, but standing wave solutions could not be constructed by the standard arguments due to the critical singularity i...
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| Veröffentlicht in: | Calculus of variations and partial differential equations 2023-03, Vol.62 (2), Article 57 |
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| container_title | Calculus of variations and partial differential equations |
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| creator | Huh, Hyungjin Han, Jongmin Jin, Sangdon |
| description | We prove the existence of standing wave solutions for the Maxwell–Chern–Simons–Schrödinger equation. This model describes the fractional quantum Hall effect and anyonic superconductivity, but standing wave solutions could not be constructed by the standard arguments due to the critical singularity in the gauge fields. To overcome this difficulty, we introduce a perturbation argument by means of the Chern–Simons term. Then our result is established by applying a limiting argument and the mountain pass theorem to a functional that is obtained by representing the gauge fields in terms of a scalar field. |
| doi_str_mv | 10.1007/s00526-022-02394-2 |
| format | Article |
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This model describes the fractional quantum Hall effect and anyonic superconductivity, but standing wave solutions could not be constructed by the standard arguments due to the critical singularity in the gauge fields. To overcome this difficulty, we introduce a perturbation argument by means of the Chern–Simons term. Then our result is established by applying a limiting argument and the mountain pass theorem to a functional that is obtained by representing the gauge fields in terms of a scalar field.</description><identifier>ISSN: 0944-2669</identifier><identifier>EISSN: 1432-0835</identifier><identifier>DOI: 10.1007/s00526-022-02394-2</identifier><language>eng</language><publisher>Berlin/Heidelberg: Springer Berlin Heidelberg</publisher><subject>Analysis ; Calculus of Variations and Optimal Control; Optimization ; Control ; Mathematical and Computational Physics ; Mathematics ; Mathematics and Statistics ; Perturbation ; Quantum Hall effect ; Scalars ; Schrodinger equation ; Standing waves ; Superconductivity ; Systems Theory ; Theoretical</subject><ispartof>Calculus of variations and partial differential equations, 2023-03, Vol.62 (2), Article 57</ispartof><rights>The Author(s), under exclusive licence to Springer-Verlag GmbH Germany, part of Springer Nature 2022. 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Var</addtitle><description>We prove the existence of standing wave solutions for the Maxwell–Chern–Simons–Schrödinger equation. This model describes the fractional quantum Hall effect and anyonic superconductivity, but standing wave solutions could not be constructed by the standard arguments due to the critical singularity in the gauge fields. To overcome this difficulty, we introduce a perturbation argument by means of the Chern–Simons term. Then our result is established by applying a limiting argument and the mountain pass theorem to a functional that is obtained by representing the gauge fields in terms of a scalar field.</description><subject>Analysis</subject><subject>Calculus of Variations and Optimal Control; Optimization</subject><subject>Control</subject><subject>Mathematical and Computational Physics</subject><subject>Mathematics</subject><subject>Mathematics and Statistics</subject><subject>Perturbation</subject><subject>Quantum Hall effect</subject><subject>Scalars</subject><subject>Schrodinger equation</subject><subject>Standing waves</subject><subject>Superconductivity</subject><subject>Systems Theory</subject><subject>Theoretical</subject><issn>0944-2669</issn><issn>1432-0835</issn><fulltext>true</fulltext><rsrctype>article</rsrctype><creationdate>2023</creationdate><recordtype>article</recordtype><recordid>eNp9kE1OwzAQhS0EEqVwAVaRWAfGdjyul6jiTyoCCVhbruvQVGnS2gmFHXfgLlyAm3ASnAaJHQvr2eP3jcePkGMKpxRAngUAwTAFxuLiKkvZDhnQjMfjiItdMgCVxSKi2icHISwAqBixbEDuHxpTzYrqOdmYF5eEumyboq5C0tRJM3fJrXnduLL8fv8Yz52voj4Uy3jfbezcf312rPOJW7dmCx6SvdyUwR396pA8XV48jq_Tyd3Vzfh8kloG0KRcKSYddblAnOJUZjCK0yHL0fKpEpJHVcARpVM8z9AKRtHM0Fo2kzl1fEhO-r4rX69bFxq9qFtfxSc1k0IqCagwuljvsr4Owbtcr3yxNP5NU9BdcrpPTsfk9DY5zSLEeyhEc_e7v9b_UD8A_3RN</recordid><startdate>20230301</startdate><enddate>20230301</enddate><creator>Huh, Hyungjin</creator><creator>Han, Jongmin</creator><creator>Jin, Sangdon</creator><general>Springer Berlin Heidelberg</general><general>Springer Nature B.V</general><scope>AAYXX</scope><scope>CITATION</scope><scope>JQ2</scope><orcidid>https://orcid.org/0000-0001-9289-0255</orcidid></search><sort><creationdate>20230301</creationdate><title>Standing wave solutions to the Maxwell–Chern–Simons–Schrödinger equations</title><author>Huh, Hyungjin ; Han, Jongmin ; Jin, Sangdon</author></sort><facets><frbrtype>5</frbrtype><frbrgroupid>cdi_FETCH-LOGICAL-c200t-39927e1ef566b6b740826662f6c3b95736c3903667e93f46c5216ad6cc2d7f1e3</frbrgroupid><rsrctype>articles</rsrctype><prefilter>articles</prefilter><language>eng</language><creationdate>2023</creationdate><topic>Analysis</topic><topic>Calculus of Variations and Optimal Control; Optimization</topic><topic>Control</topic><topic>Mathematical and Computational Physics</topic><topic>Mathematics</topic><topic>Mathematics and Statistics</topic><topic>Perturbation</topic><topic>Quantum Hall effect</topic><topic>Scalars</topic><topic>Schrodinger equation</topic><topic>Standing waves</topic><topic>Superconductivity</topic><topic>Systems Theory</topic><topic>Theoretical</topic><toplevel>peer_reviewed</toplevel><toplevel>online_resources</toplevel><creatorcontrib>Huh, Hyungjin</creatorcontrib><creatorcontrib>Han, Jongmin</creatorcontrib><creatorcontrib>Jin, Sangdon</creatorcontrib><collection>CrossRef</collection><collection>ProQuest Computer Science Collection</collection><jtitle>Calculus of variations and partial differential equations</jtitle></facets><delivery><delcategory>Remote Search Resource</delcategory><fulltext>fulltext</fulltext></delivery><addata><au>Huh, Hyungjin</au><au>Han, Jongmin</au><au>Jin, Sangdon</au><format>journal</format><genre>article</genre><ristype>JOUR</ristype><atitle>Standing wave solutions to the Maxwell–Chern–Simons–Schrödinger equations</atitle><jtitle>Calculus of variations and partial differential equations</jtitle><stitle>Calc. Var</stitle><date>2023-03-01</date><risdate>2023</risdate><volume>62</volume><issue>2</issue><artnum>57</artnum><issn>0944-2669</issn><eissn>1432-0835</eissn><abstract>We prove the existence of standing wave solutions for the Maxwell–Chern–Simons–Schrödinger equation. This model describes the fractional quantum Hall effect and anyonic superconductivity, but standing wave solutions could not be constructed by the standard arguments due to the critical singularity in the gauge fields. To overcome this difficulty, we introduce a perturbation argument by means of the Chern–Simons term. Then our result is established by applying a limiting argument and the mountain pass theorem to a functional that is obtained by representing the gauge fields in terms of a scalar field.</abstract><cop>Berlin/Heidelberg</cop><pub>Springer Berlin Heidelberg</pub><doi>10.1007/s00526-022-02394-2</doi><orcidid>https://orcid.org/0000-0001-9289-0255</orcidid></addata></record> |
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| subjects | Analysis Calculus of Variations and Optimal Control Optimization Control Mathematical and Computational Physics Mathematics Mathematics and Statistics Perturbation Quantum Hall effect Scalars Schrodinger equation Standing waves Superconductivity Systems Theory Theoretical |
| title | Standing wave solutions to the Maxwell–Chern–Simons–Schrödinger equations |
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