论文标题
特殊点的汇合和量子灾难的系统分类
Confluences of exceptional points and a systematic classification of quantum catastrophes
论文作者
论文摘要
假定我们利益的特定量子相变与封闭的统一量子系统的掉落有关的特殊点（EP）奇异性。这种“量子灾难”的物理实现（通常是连接的，与相应参数有关的哈密顿$ H（g）$的对角度瞬间丧失自然地取决于EP的形式数学特征，即所谓的Algebraic yelcity $ n $ $ n $ beforcial $ n $ n $ bexircial $ n $ bexircial。在我们的论文中，我们假设它们都是有限的，我们使用几种可解决的玩具模型来说明和讨论EP-MERGER实现的某些最基本的机制，即过渡$ g \ to g^{（ep）} $的过程。
Specific quantum phase transitions of our interest are assumed associated with the fall of a closed, unitary quantum system into its exceptional-point (EP) singularity. The physical realization of such a "quantum catastrophe" (connected, typically, with an instantaneous loss of the diagonalizability of the corresponding parameter-dependent Hamiltonian $H(g)$) depends, naturally, on the formal mathematical characteristics of the EP, i.e., in essence, on its so called algebraic multiplicity $N$ and geometric multiplicity $K$. In our paper we assume that both of them are finite, and we illustrate and discuss, using several solvable toy models, some of the most elementary mechanisms of the EP-merger realization of the process of the transition $g \to g^{(EP)}$.
