In an overall framework of quantum mechanics of unitary systems a rather sophisticated new version of perturbation theory is developed. What is assumed is, firstly, that the perturbed Hamiltonians $H=H_0+\lambda V$ are non-Hermitian and lie close to their unobservable exceptional-point (EP) degeneracy limit $H_0$. Secondly, in this EP limit, the geometric multiplicity $L$ of the degenerate unperturbed eigenvalue $E_0$ is assumed, in contrast to the majority of existing studies, larger than one. Under these assumptions the method of construction of the bound states is described. Its specific subtleties are illustrated via the leading-order recipe. The emergence of a counterintuitive connection between the value of $L$, the structure of the matrix elements of perturbations, and the possible loss of the stability and unitarity of the processes of the unfolding of the EP singularity is given a detailed explanation.

中文翻译：

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近退化异常点的微扰理论

在幺正系统的量子力学的总体框架中，开发了一种相当复杂的新版本的微扰理论。首先假设扰动的哈密顿量 $H=H_0+\lambda V$ 是非 Hermitian 并且接近于它们不可观察的异常点 (EP) 简并极限 $H_0$。其次，在这个 EP 限制中，与大多数现有研究相比，假设退化未扰动特征值 $E_0$ 的几何多重性 $L$ 大于 1。在这些假设下，描述了约束状态的构造方法。它的具体微妙之处通过前导配方说明。$L$ 的值与扰动矩阵元素的结构之间出现了违反直觉的联系，