Adjacency graphs and long-range interactions of atoms in quasi-degenerate states: applied graph theory
Adjacency graphs and long-range interactions of atoms in quasi-degenerate states: applied graph theory
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准简并态原子的邻接图和长程相互作用：应用图论
DOI：
10.1007/s00340-016-6587-5
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发表时间：
2016
期刊：
影响因子：
--
通讯作者：
U. Jentschura
中科院分区：
文献类型：
--
作者：
C. Adhikari;V. Debierre;U. Jentschura
我们分析，在一般情况下，在量子力学中的能级的演化，作为一个耦合参数的函数，并证明了不可约矩阵描述的系统中的水平交叉的可能性。在长程相互作用中，耦合参数是原子间距离。我们展示了实用程序的邻接矩阵和邻接图中的“隐藏”的对称性的问题的分析，这些使我们能够将可约矩阵分解成不可约的子组件。指出了高维不可约矩阵不相交定理的一个可能的失效，并简要地描述了它在氢原子2S-2S相互作用中的应用。该系统中原子间相互作用的分析对于进一步开展2S超精细分裂的光学测量具有重要意义。
We analyze, in general terms, the evolution of energy levels in quantum mechanics, as a function of a coupling parameter, and demonstrate the possibility of level crossings in systems described by irreducible matrices. In long-range interactions, the coupling parameter is the interatomic distance. We demonstrate the utility of adjacency matrices and adjacency graphs in the analysis of “hidden” symmetries of a problem; these allow us to break reducible matrices into irreducible subcomponents. A possible breakdown of the no-crossing theorem for higher-dimensional irreducible matrices is indicated, and an application to the 2S–2S interaction in hydrogen is briefly described. The analysis of interatomic interactions in this system is important for further progress on optical measurements of the 2S hyperfine splitting.