动力学局部化的微扰分析
Perturbative Analysis of Dynamical Localisation
摘要：
本文推广了关于一类周期含时二能级系统薛定谔方程的收敛微扰解的已有结果。这里处理的情况是特别适合于调查的两级系统表现出的现象（近似）动态本地化。我们还提出了一个收敛的微扰扩展的长期频率，并详细讨论了单色相互作用（交流-直流领域）的特殊情况下，提供了一个完整的微扰解决方案的情况下。我们的方法是基于一个“重正化”的过程，我们在这里以更系统的方式开发。由于没有长期的条款和一致收敛的时间，我们的扩展允许严格的研究这种系统的长期行为，也非常适合于数值计算，因为我们简要讨论，导致非常准确的计算量，如跃迁概率很长一段时间相比，外部场的周期。
英文摘要：
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.
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