We review various unitary time-dependent perturbation theories and compare them formally and numerically. We show that the Kolmogorov-Arnold-Moser technique performs better owing to both the superexponential character of correction terms and the possibility to optimize the accuracy of a given level of approximation which is explored in details here. As an illustration, we consider a two-level system driven by short pulses beyond the sudden limit.
@article{arxiv.quant-ph/0401084,
title = {Pulse-driven quantum dynamics beyond the impulsive regime},
author = {D. Daems and S. Guérin and H. R. Jauslin and A. Keller and O. Atabek},
journal= {arXiv preprint arXiv:quant-ph/0401084},
year = {2007}
}