Asymptotic behavior of large eigenvalues of Jaynes-Cummings type models

被引：7

作者：

de Monvel, Anne Boutet ^{[1
]}

Zielinski, Lech ^{[2
]}

机构：

[1] Univ Paris Diderot, Inst Math Jussieu PRG, Bat Sophie Germain,Case 7012, F-75205 Paris 13, France

[2] Univ Littoral, LMPA, 50 Rue Ferdinand Buisson,CS 80699, F-62228 Calais, France

来源：

JOURNAL OF SPECTRAL THEORY | 2017年 / 7卷 / 02期

关键词：

Jacobi matrices; Jaynes-Cummings model; eigenvalue estimates; UNBOUNDED JACOBI MATRICES; APPROXIMATION;

D O I：

10.4171/JST/172

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

We consider a class of unbounded self-adjoint operators including the Hamiltonian of the Jaynes-Cummings model without the rotating-wave approximation (RWA). The corresponding operators are defined by infinite Jacobimatriceswith discrete spectrum. Our purpose is to give the asymptotic behavior of large eigenvalues.

引用

页码：559 / 631

页数：73

共 10 条

[1] [Anonymous], OPER THEORY ADV APPL
[2] Cojuhari PA, 2007, ACTA SCI MATH, V73, P649
[3] de Monvel A. Boutet, 2008, PREPRINT
[4] de Monvel A. Boutet, 2014, AM MATH SOC T SERIES, V66, P77
[5] de Monvel AB, 2006, ASYMPTOTIC ANAL, V47, P291
[6] Approximation of eigenvalues for unbounded Jacobi matrices using finite submatrices
de Monvel, Anne Boutet
Zielinski, Lech
[J]. CENTRAL EUROPEAN JOURNAL OF MATHEMATICS, 2014, 12 (03): : 445 - 463
[7] Infinite Jacobi matrices with unbounded entries: Asymptotics of eigenvalues and the transformation operator approach
Janas, J
Naboko, S
[J]. SIAM JOURNAL ON MATHEMATICAL ANALYSIS, 2004, 36 (02) : 643 - 658
[8] Asymptotics of large eigenvalues for some discrete unbounded Jacobi matrices
Malejki, Maria
[J]. LINEAR ALGEBRA AND ITS APPLICATIONS, 2009, 431 (10) : 1952 - 1970
[9] Jaynes-Cummings model:: Solutions without rotating-wave approximation
Tur, ÉA
[J]. OPTICS AND SPECTROSCOPY, 2000, 89 (04) : 574 - 588
[10] Yanovich E. A., 2013, OPERATOR THEORY ADV, V227, P165

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