Eigenvalue asymptotics of a modified Jaynes–Cummings model with periodic modulations |
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| Authors: | Anne Boutet de Monvel Serguei Naboko Luis O. Silva |
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| Affiliation: | 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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| Abstract: | 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. To cite this article: A. Boutet de Monvel et al., C. R. Acad. Sci. Paris, Ser. I 338 (2004). |
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