论文标题
扰动理论接近堕落的特殊点
Perturbation theory near degenerate exceptional points
论文作者
论文摘要
在统一系统的量子力学的总体框架中，开发了相当复杂的新版本的扰动理论。首先，假定的是扰动的汉密尔顿人$ h = h_0+λv$是非热的，并且靠近其无法观察到的异常点（EP）堕落限制限制$ h_0 $。其次，在此EP限制中，假定退化不受干扰的特征值$ e_0 $的几何多重性$ l $与大多数现有研究相反，大于一个。在这些假设下，描述了结合状态的构建方法。它的特定微妙之处是通过领先配方说明的。 $ l $的值，扰动矩阵元素的结构以及稳定性和单位性的可能损失的损失和单位性的损失得到了详细的解释。
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 $H=H_0+λV$ 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.
