Mathematical Physics
Eigenvalue asymptotics of a modified Jaynes–Cummings model with periodic modulations
Comptes Rendus. Mathématique, Volume 338 (2004) no. 1, pp. 103-107.

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 nth eigenvalue λn as n→∞ 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.

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 n→+∞, de la nième valeur propre λn, 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.

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DOI: 10.1016/j.crma.2003.12.001
Boutet de Monvel, Anne 1; Naboko, Serguei 2; Silva, Luis O. 3

1 Institut de mathématiques de Jussieu, case 7012, Université Paris 7, 2, place Jussieu, 75251 Paris, France
2 Department of Higher Mathematics and Mathematical Physics, Institute of Physics, St. Petersburg State University, 1 Ulianovskaya 198904, St. Petersburg, Russia
3 Department 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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     title = {Eigenvalue asymptotics of a modified {Jaynes{\textendash}Cummings} model with periodic modulations},
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Boutet de Monvel, Anne; Naboko, Serguei; Silva, Luis O. Eigenvalue asymptotics of a modified Jaynes–Cummings model with periodic modulations. Comptes Rendus. Mathématique, Volume 338 (2004) no. 1, pp. 103-107. doi : 10.1016/j.crma.2003.12.001. http://www.numdam.org/articles/10.1016/j.crma.2003.12.001/

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