Asymptotic behavior of large eigenvalues of Jaynes-Cummings type models

Abstract

We consider a class of unbounded self-adjoint operators including the Hamiltonian of the Jaynes-Cummings model without the rotating-wave approximation (RWA). The corresponding operators are defined by infinite Jacobi matrices with discrete spectrum. Our purpose is to give the asymptotic behavior of large eigenvalues.

47 pages, no figure