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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Anne Boutet de Monvel 1; Serguei Naboko 2; Luis O. Silva 3
@article{CRMATH_2004__338_1_103_0, author = {Anne Boutet de Monvel and Serguei Naboko and Luis O. Silva}, 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}, }
TY - JOUR AU - Anne Boutet de Monvel AU - Serguei Naboko AU - Luis O. Silva 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 DO - 10.1016/j.crma.2003.12.001 LA - en ID - CRMATH_2004__338_1_103_0 ER -
%0 Journal Article %A Anne Boutet de Monvel %A Serguei Naboko %A Luis O. Silva %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 %R 10.1016/j.crma.2003.12.001 %G en %F CRMATH_2004__338_1_103_0
Anne Boutet de Monvel; Serguei Naboko; Luis O. Silva. 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. https://comptes-rendus.academie-sciences.fr/mathematique/articles/10.1016/j.crma.2003.12.001/
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