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Comptes Rendus Mathématique
Volume 338, n° 1
pages 103-107 (janvier 2004)
Doi : 10.1016/j.crma.2003.12.001
Received : 26 September 2003 ;  accepted : 1 December 2003
Eigenvalue asymptotics of a modified Jaynes-Cummings model with periodic modulations

Anne  Boutet de Monvel a ,  Serguei  Naboko b ,  Luis O.  Silva c
aInstitut de mathématiques de Jussieu, case 7012, Université Paris 7, 2, place Jussieu, 75251 Paris, France 
bDepartment of Higher Mathematics and Mathematical Physics, Institute of Physics, St. Petersburg State University, 1 Ulianovskaya 198904, St. Petersburg, Russia 
cDepartment of Mathematical and Numerical Methods, IIMAS, Universidad Nacional Autónoma de México, Apdo. postal 20-726, C.P. 01000, México D.F., Mexico 

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We analyze the influence of additive and multiplicative periodic modulations on the asymptotic behavior of eigenvalues of some Hermitian Jacobi Matrices related to the Jaynes-Cummings model using the so-called “successive diagonalization” method. This approach allows us to find the asymptotics of the  th eigenvalue   as   stepwise with successively increasing precision. We bring to light the interplay of additive and multiplicative periodic modulations and their influence on the asymptotic behavior of eigenvalues. To cite this article: A. Boutet de Monvel et al., C. R. Acad. Sci. Paris, Ser. I 338 (2004).

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L'objet de cette Note est d'analyser l'effet de modulations périodiques additives et multiplicatives sur le comportement asymptotique des valeurs propres de matrices de Jacobi liées au modèle de Jaynes-Cummings. Nous utilisons une méthode « de diagonalisations successives » pour obtenir le comportement asymptotique, pour  , de la  ième valeur propre  , celles-ci étant supposées rangées par ordre croissant. Les résultats obtenus mettent en évidence l'effet des modulations périodiques considérées sur le comportement asymptotique des valeurs propres. Pour citer cet article : A. Boutet de Monvel et al., C. R. Acad. Sci. Paris, Ser. I 338 (2004).




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