In quantum mechanics, the Rosen-Zener model represents a two-level quantum system. Its generalization to multiple degenerate sets of states leads to larger non-autonomous linear system of ordinary differential equations (ODEs). We propose a new method for computing the solution operator of this system of ODEs. This new method is based on a recently introduced expression of the solution in terms of an infinite matrix equation, which can be efficiently approximated by combining truncation, fixed point iterations, and low-rank approximation. This expression is possible thanks to the so-called $\star$-product approach for linear ODEs. In the numerical experiments, the new method's computing time scales linearly with the model's size. We provide a first partial explanation of this linear behavior.

翻译：在量子力学中，Rosen-Zener模型描述了一个两能级量子系统。将其推广到多重简并态集合会导致更大规模的非自治线性常微分方程组。我们提出了一种计算该常微分方程组解算子的新方法。该方法基于近期引入的以无限矩阵方程形式表达的解，可通过截断、不动点迭代与低秩近似相结合实现高效逼近。该表达形式得益于线性常微分方程中的所谓$\star$-积方法。数值实验表明，新方法的计算时间随模型规模呈线性增长。我们对该线性行为给出了初步解释。