We discuss a class of models that generalize the two-state Landau–Zener Hamiltonian to both the multistate and multitime evolution. It is already known that the corresponding quantum mechanical evolution can be understood in great detail. Here, we present an approach to classify such solvable models, namely, to identify all their independent families for a given number N of interacting states and prove the absence of such families for some types of interactions. We also discuss how, within a solvable family, one can classify the scattering matrices, i.e., the system’s dynamics. Due to the possibility of such a detailed classification, the multitime Landau–Zener model defines a useful special function of theoretical physics.

中文翻译：

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多次Landau–Zener模型：可解哈密顿量的分类

我们讨论了将两态Landau-Zener哈密顿量推广到多态和多时演化的模型。众所周知，可以非常详细地理解相应的量子力学演化。在这里，我们提出一种对此类可解决模型进行分类的方法，即针对给定数量的N个交互状态识别所有其独立的族，并证明对于某些类型的交互不存在此类族。我们还将讨论在一个可解决的族中如何对散射矩阵进行分类，即系统的动力学。由于可以进行详细分类，因此多次Landau-Zener模型定义了理论物理学的有用特殊功能。