Combinatorial approach to Mathieu and Lame equations
Autor(a) principal: | |
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Data de Publicação: | 2015 |
Tipo de documento: | Artigo |
Idioma: | eng |
Título da fonte: | Repositório Institucional da UNESP |
Texto Completo: | http://dx.doi.org/10.1063/1.4926954 http://hdl.handle.net/11449/160689 |
Resumo: | Based on some recent progress on a relation between four dimensional super Yang-Mills gauge theory and quantum integrable system, we study the asymptotic spectrum of the quantum mechanical problems described by the Mathieu equation and the Lame equation. The large momentum asymptotic expansion of the eigenvalue is related to the instanton partition function of supersymmetric gauge theories which can be evaluated by a combinatorial method. The electro-magnetic duality of gauge theory indicates that in the parameter space, there are three asymptotic expansions for the eigenvalue, and we confirm this fact by performing the Wentzel-Kramers-Brillouin (WKB) analysis in each asymptotic expansion region. The results presented here give some new perspective on the Floquet theory about periodic differential equation. (C) 2015 AIP Publishing LLC. |
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Combinatorial approach to Mathieu and Lame equationsBased on some recent progress on a relation between four dimensional super Yang-Mills gauge theory and quantum integrable system, we study the asymptotic spectrum of the quantum mechanical problems described by the Mathieu equation and the Lame equation. The large momentum asymptotic expansion of the eigenvalue is related to the instanton partition function of supersymmetric gauge theories which can be evaluated by a combinatorial method. The electro-magnetic duality of gauge theory indicates that in the parameter space, there are three asymptotic expansions for the eigenvalue, and we confirm this fact by performing the Wentzel-Kramers-Brillouin (WKB) analysis in each asymptotic expansion region. The results presented here give some new perspective on the Floquet theory about periodic differential equation. (C) 2015 AIP Publishing LLC.NSFC through ZJU, ChinaFundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP)Zhejiang Univ, Ctr Math Sci, Hangzhou 310027, Zhejiang, Peoples R ChinaUniv Estadual Paulista, Inst Fis Teor, BR-01140070 Sao Paulo, SP, BrazilUniv Estadual Paulista, Inst Fis Teor, BR-01140070 Sao Paulo, SP, BrazilNSFC through ZJU, China: 11031005FAPESP: 2011/21812-8Amer Inst PhysicsZhejiang UnivUniversidade Estadual Paulista (Unesp)He, Wei [UNESP]2018-11-26T16:16:19Z2018-11-26T16:16:19Z2015-07-01info:eu-repo/semantics/publishedVersioninfo:eu-repo/semantics/article22application/pdfhttp://dx.doi.org/10.1063/1.4926954Journal Of Mathematical Physics. Melville: Amer Inst Physics, v. 56, n. 7, 22 p., 2015.0022-2488http://hdl.handle.net/11449/16068910.1063/1.4926954WOS:000358932300026WOS000358932300026.pdfWeb of Sciencereponame:Repositório Institucional da UNESPinstname:Universidade Estadual Paulista (UNESP)instacron:UNESPengJournal Of Mathematical Physics0,644info:eu-repo/semantics/openAccess2023-12-12T06:16:42Zoai:repositorio.unesp.br:11449/160689Repositório InstitucionalPUBhttp://repositorio.unesp.br/oai/requestopendoar:29462024-08-05T20:05:55.276431Repositório Institucional da UNESP - Universidade Estadual Paulista (UNESP)false |
dc.title.none.fl_str_mv |
Combinatorial approach to Mathieu and Lame equations |
title |
Combinatorial approach to Mathieu and Lame equations |
spellingShingle |
Combinatorial approach to Mathieu and Lame equations He, Wei [UNESP] |
title_short |
Combinatorial approach to Mathieu and Lame equations |
title_full |
Combinatorial approach to Mathieu and Lame equations |
title_fullStr |
Combinatorial approach to Mathieu and Lame equations |
title_full_unstemmed |
Combinatorial approach to Mathieu and Lame equations |
title_sort |
Combinatorial approach to Mathieu and Lame equations |
author |
He, Wei [UNESP] |
author_facet |
He, Wei [UNESP] |
author_role |
author |
dc.contributor.none.fl_str_mv |
Zhejiang Univ Universidade Estadual Paulista (Unesp) |
dc.contributor.author.fl_str_mv |
He, Wei [UNESP] |
description |
Based on some recent progress on a relation between four dimensional super Yang-Mills gauge theory and quantum integrable system, we study the asymptotic spectrum of the quantum mechanical problems described by the Mathieu equation and the Lame equation. The large momentum asymptotic expansion of the eigenvalue is related to the instanton partition function of supersymmetric gauge theories which can be evaluated by a combinatorial method. The electro-magnetic duality of gauge theory indicates that in the parameter space, there are three asymptotic expansions for the eigenvalue, and we confirm this fact by performing the Wentzel-Kramers-Brillouin (WKB) analysis in each asymptotic expansion region. The results presented here give some new perspective on the Floquet theory about periodic differential equation. (C) 2015 AIP Publishing LLC. |
publishDate |
2015 |
dc.date.none.fl_str_mv |
2015-07-01 2018-11-26T16:16:19Z 2018-11-26T16:16:19Z |
dc.type.status.fl_str_mv |
info:eu-repo/semantics/publishedVersion |
dc.type.driver.fl_str_mv |
info:eu-repo/semantics/article |
format |
article |
status_str |
publishedVersion |
dc.identifier.uri.fl_str_mv |
http://dx.doi.org/10.1063/1.4926954 Journal Of Mathematical Physics. Melville: Amer Inst Physics, v. 56, n. 7, 22 p., 2015. 0022-2488 http://hdl.handle.net/11449/160689 10.1063/1.4926954 WOS:000358932300026 WOS000358932300026.pdf |
url |
http://dx.doi.org/10.1063/1.4926954 http://hdl.handle.net/11449/160689 |
identifier_str_mv |
Journal Of Mathematical Physics. Melville: Amer Inst Physics, v. 56, n. 7, 22 p., 2015. 0022-2488 10.1063/1.4926954 WOS:000358932300026 WOS000358932300026.pdf |
dc.language.iso.fl_str_mv |
eng |
language |
eng |
dc.relation.none.fl_str_mv |
Journal Of Mathematical Physics 0,644 |
dc.rights.driver.fl_str_mv |
info:eu-repo/semantics/openAccess |
eu_rights_str_mv |
openAccess |
dc.format.none.fl_str_mv |
22 application/pdf |
dc.publisher.none.fl_str_mv |
Amer Inst Physics |
publisher.none.fl_str_mv |
Amer Inst Physics |
dc.source.none.fl_str_mv |
Web of Science reponame:Repositório Institucional da UNESP instname:Universidade Estadual Paulista (UNESP) instacron:UNESP |
instname_str |
Universidade Estadual Paulista (UNESP) |
instacron_str |
UNESP |
institution |
UNESP |
reponame_str |
Repositório Institucional da UNESP |
collection |
Repositório Institucional da UNESP |
repository.name.fl_str_mv |
Repositório Institucional da UNESP - Universidade Estadual Paulista (UNESP) |
repository.mail.fl_str_mv |
|
_version_ |
1808129159393705984 |