Znojil Miloslav
The Czech Academy of Sciences, Nuclear Physics Institute, Hlavní 130, 250 68 Řež, Czech Republic and Department of Physics, Faculty of Science, University of Hradec Králové, Rokitanského 62, 50003 Hradec Králové, Czech Republic.
Phys Rev E. 2021 Mar;103(3-1):032120. doi: 10.1103/PhysRevE.103.032120.
The phenomenon of degeneracy of an N-plet of bound states is studied in the framework of the quasi-Hermitian (a.k.a. PT-symmetric) formulation of quantum theory of closed systems. For a general non-Hermitian Hamiltonian H=H(λ) such a degeneracy may occur at a real Kato's exceptional point λ^{(EPN)} of order N and of the geometric multiplicity alias clusterization index K. The corresponding unitary process of collapse (loss of observability) can be then interpreted as a generic quantum phase transition. The dedicated literature deals, predominantly, with the non-numerical benchmark models of the simplest processes where K=1. In our present paper it is shown that in the "anomalous" dynamical scenarios with 1<K≤N/2 an analogous approach is applicable. A multiparametric anharmonic-oscillator-type exemplification of such systems is constructed as a set of real-matrix N by N Hamiltonians which are exactly solvable, maximally non-Hermitian, and labeled by specific ad hoc partitionings R(N) of N.
在封闭系统量子理论的准厄米（又称PT对称）表述框架下，研究了N重束缚态的简并现象。对于一般的非厄米哈密顿量H = H(λ)，这种简并可能发生在阶数为N且几何重数别名聚类指数为K的实加藤例外点λ^(EPN)处。相应的坍缩（可观测性丧失）酉过程随后可解释为一般的量子相变。专门文献主要讨论K = 1的最简单过程的非数值基准模型。在我们目前的论文中表明，在1 < K ≤ N/2的“反常”动力学情形中，类似方法是适用的。此类系统的多参数非简谐振荡器型示例被构建为一组N×N实矩阵哈密顿量，它们是精确可解的、最大非厄米的，并由N的特定特设划分R(N)标记。
