[Effet de modulations périodiques sur l'asymptotique des valeurs propres d'une variante du modèle de Jaynes–Cummings]
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.
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.
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@article{CRMATH_2004__338_1_103_0,
author = {Boutet de Monvel, Anne and Naboko, Serguei and Silva, Luis O.},
title = {Eigenvalue asymptotics of a modified {Jaynes{\textendash}Cummings} model with periodic modulations},
journal = {Comptes Rendus. Math\'ematique},
pages = {103--107},
publisher = {Elsevier},
volume = {338},
number = {1},
year = {2004},
doi = {10.1016/j.crma.2003.12.001},
language = {en},
url = {http://www.numdam.org/articles/10.1016/j.crma.2003.12.001/}
}
TY - JOUR AU - Boutet de Monvel, Anne AU - Naboko, Serguei AU - Silva, Luis O. TI - Eigenvalue asymptotics of a modified Jaynes–Cummings model with periodic modulations JO - Comptes Rendus. Mathématique PY - 2004 SP - 103 EP - 107 VL - 338 IS - 1 PB - Elsevier UR - http://www.numdam.org/articles/10.1016/j.crma.2003.12.001/ DO - 10.1016/j.crma.2003.12.001 LA - en ID - CRMATH_2004__338_1_103_0 ER -
%0 Journal Article %A Boutet de Monvel, Anne %A Naboko, Serguei %A Silva, Luis O. %T Eigenvalue asymptotics of a modified Jaynes–Cummings model with periodic modulations %J Comptes Rendus. Mathématique %D 2004 %P 103-107 %V 338 %N 1 %I Elsevier %U http://www.numdam.org/articles/10.1016/j.crma.2003.12.001/ %R 10.1016/j.crma.2003.12.001 %G en %F CRMATH_2004__338_1_103_0
Boutet de Monvel, Anne; Naboko, Serguei; Silva, Luis O. Eigenvalue asymptotics of a modified Jaynes–Cummings model with periodic modulations. Comptes Rendus. Mathématique, Tome 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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