Emergence and localization of exceptional points in an exactly solvable toy model
Fuente:
arXiv
Saved in:
| Main Author: | |
|---|---|
| Format: | Preprint |
| Published: |
2025
|
| Subjects: | |
| Online Access: | |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| _version_ | 1866914071598596096 |
|---|---|
| author | Znojil, Miloslav |
| author_facet | Znojil, Miloslav |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2510_01756 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Emergence and localization of exceptional points in an exactly solvable toy model Znojil, Miloslav Quantum Physics 81Q12 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. |
| title | Emergence and localization of exceptional points in an exactly solvable toy model |
| topic | Quantum Physics 81Q12 |
| url | https://arxiv.org/abs/2510.01756 |