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(Referência obtida automaticamente do Web of Science, por meio da informação sobre o financiamento pela FAPESP e o número do processo correspondente, incluída na publicação pelos autores.)

Combinatorial approach to Mathieu and Lame equations

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Autor(es):
He, Wei [1, 2]
Número total de Autores: 1
Afiliação do(s) autor(es):
[1] Univ Estadual Paulista, Inst Fis Teor, BR-01140070 Sao Paulo, SP - Brazil
[2] Zhejiang Univ, Ctr Math Sci, Hangzhou 310027, Zhejiang - Peoples R China
Número total de Afiliações: 2
Tipo de documento: Artigo Científico
Fonte: Journal of Mathematical Physics; v. 56, n. 7 JUL 2015.
Citações Web of Science: 4
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. (AU)

Processo FAPESP: 11/21812-8 - Teoria quântica de campos e sistemas integráveis
Beneficiário:Wei He
Linha de fomento: Bolsas no Brasil - Pós-Doutorado