两个非束缚态简并点的展开：能量和宽度的交叉和反交叉
Unfolding a degeneracy point of two unbound states: Crossings and anticrossings of energies and widths
摘要：
我们表明，当一个孤立的双重束缚态的物理系统成为退化的某些值的控制参数的系统，能量超曲面表示的复杂的共振能量本征值作为控制参数的函数在参数空间中有一个代数分支点的秩为1。与参数空间中的这种奇异性相关联的散射矩阵S_l（E）和格林函数G_l^（+）（k; r，r '）在复能量平面的非物理层中具有一个双极点。我们通过一个通用的2-参数函数族来描述参数空间中两个非束缚态的典型简并点的通用展开或变形，该函数族与孤立的双重共振在例外点处的极点位置函数是接触等价的，并且包括简并条件的所有小扰动直到接触等价。
英文摘要：
We show that when an isolated doublet of unbound states of a physical system becomes degenerate for some values of the control parameters of the system, the energy hypersurfaces representing the complex resonance energy eigenvalues as functions of the control parameters have an algebraic branch point of rank one in parameter space. Associated with this singularity in parameter space, the scattering matrix, S_l(E), and the Green's function, G_l^(+)(k; r,r'), have one double pole in the unphysical sheet of the complex energy plane. We characterize the universal unfolding or deformation of a typical degeneracy point of two unbound states in parameter space by means of a universal 2-parameter family of functions which is contact equivalent to the pole position function of the isolated doublet of resonances at the exceptional point and includes all small perturbations of the degeneracy condition up to contact equivalence.
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