Physics – Mathematical Physics
Scientific paper
2002-01-03
J.Math.Phys. 44 (2003) 1937-1960
Physics
Mathematical Physics
45 pages, 4 figures. Minor corrections in Section 5 and added Appendix D
Scientific paper
In this paper we extend previous results on convergent perturbative solutions of the Schroedinger equation of a class of periodically time-dependent two-level systems. The situation treated here is particularly suited for the investigation of two-level systems exhibiting the phenomenon of (approximate) dynamical localisation. We also present a convergent perturbative expansion for the secular frequency and discuss in detail the particular case of monochromatic interactions (ac-dc fields), providing a complete perturbative solution for that case. Our method is based on a ``renormalisation'' procedure, which we develop in a more systematic way here. For being free of secular terms and uniformly convergent in time, our expansions allow a rigorous study of the long-time behaviour of such systems and are also well-suited for numerical computations, as we briefly discuss, leading to very accurate calculations of quantities like transition probabilities for very long times compared to the cycles of the external field.
Barata Joao C. A.
Cortez Daniel A.
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