The asymptotic behavior of eigenvalues of a modified Jaynes–Cummings model

Article type: Research Article

Authors: Boutet de Monvel, Anne | Naboko, Serguei^; | Silva, Luis O.^;

Affiliations: Institut de Mathématiques de Jussieu, case 7012, Université Paris 7, 2 place Jussieu, 75251 Paris, France E-mail: aboutet@math.jussieu.fr | Dept. of Mathematical Physics, Institute of Physics, St. Petersburg State University, 1 Ulianovskaya, 198904 St. Petersburg, Russia E-mail: naboko@snoopy.phys.spbu.ru | Departamento de Métodos Matemáticos y Numéricos, IIMAS, Universidad Nacional Autónoma de México, Apdo. Postal 20-726 México, D.F. 01000 E-mail: silva@leibniz.iimas.unam.mx

Note: [] Author supported by KBN grant 5 PO3A/026/21.

Note: [] Partially supported by project PAPIIT IN 101902, DGAPA-UNAM.

Abstract: We obtain the asymptotic behavior of eigenvalues of Jacobi matrices corresponding to a modified Jaynes–Cummings model with additive and multiplicative modulations using the so-called successive diagonalization method. By comparing the cases with and without modulated entries, we show the influence of periodic modulations on the eigenvalue asymptotics.

Journal: Asymptotic Analysis, vol. 47, no. 3-4, pp. 291-315, 2006