J. C. A. Barata, D. A. Cortez
Perturbative Analysis of Dynamical Localisation
(630K, Postscript)

ABSTRACT.  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.