Eigenvalue asymptotics of a modified Jaynes-Cummings model with periodic modulations

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 lambda(n) as n --> infinity 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. (C) 2003 Academie des sciences. Published by Elsevier SAS. All rights reserved.