Emergence and localization of exceptional points in an exactly solvable toy model

• URL: http://arxiv.org/abs/2510.01756v1
• Date: Thu, 02 Oct 2025 07:43:19 GMT
• Title: Emergence and localization of exceptional points in an exactly solvable toy model
• Authors: Miloslav Znojil,
• Abstract summary: The Schroedinger equation is required discrete and endowed with PT-symmetric Robin boundary conditions.<n>A not quite expected existence of a multi-band spectral structure in another simplified one-parametric family of models is also revealed.
• Score: 0.0
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: The most elementary non-Hermitian quantum square-well problem with real spectrum is considered. The Schroedinger equation is required discrete and endowed with PT-symmetric Robin (i.e., two-parametric) boundary conditions. Some of the rather enigmatic aspects of impact of the variability of the parameters on the emergence of the Kato's exceptional-point (EP) singularities is clarified. In particular, the current puzzle of the apparent absence of the EP degeneracies at the odd-matrix dimensions in certain simplified one-parametric cases is explained. A not quite expected existence of a multi-band spectral structure in another simplified one-parametric family of models is also revealed.

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