Asymptotic non-Hermitian degeneracy phenomenon and its exactly solvable simulation
Fuente:
arXiv
Salvato in:
| Autore principale: | |
|---|---|
| Natura: | Preprint |
| Pubblicazione: |
2026
|
| Soggetti: | |
| Accesso online: | |
| Tags: |
Aggiungi Tag
Nessun Tag, puoi essere il primo ad aggiungerne!!
|
| _version_ | 1866918391214768128 |
|---|---|
| author | Znojil, Miloslav |
| author_facet | Znojil, Miloslav |
| contents | Up to these days, the popular PT-symmetric imaginary cubic oscillator did not find any consistent probabilistic quantum-mechanical interpretation because its Hamiltonian has been shown, by mathematicians, intrinsic-exceptional-point (IEP) singular. In the paper we explain why there is even no reasonable small-perturbation-based regularization of the similar unacceptable (i.e., IEP-singular) quantum models. The explanation is based on a partial formal analogy of the IEP singularity with the conventional exceptional point (EP). What is important is that we are able to construct a simplified $N$ by $N$-matrix (and exactly solvable) toy-model Hamiltonian admitting the asymptotic (i.e., high-excitation) EP-related wave-function degeneracy which, in some sense (i.e., in the limit of large $N$) mimics several aspects of its IEP analogue. In this comparison, the difference is that the regularization of the EP singularities is possible (using an ad hoc perturbation of size ${\cal O}(1/N)$) while an analogous regularization of the IEP singularity is not (we have to consider $N \to \infty$). |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2603_13141 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Asymptotic non-Hermitian degeneracy phenomenon and its exactly solvable simulation Znojil, Miloslav Quantum Physics Mathematical Physics Up to these days, the popular PT-symmetric imaginary cubic oscillator did not find any consistent probabilistic quantum-mechanical interpretation because its Hamiltonian has been shown, by mathematicians, intrinsic-exceptional-point (IEP) singular. In the paper we explain why there is even no reasonable small-perturbation-based regularization of the similar unacceptable (i.e., IEP-singular) quantum models. The explanation is based on a partial formal analogy of the IEP singularity with the conventional exceptional point (EP). What is important is that we are able to construct a simplified $N$ by $N$-matrix (and exactly solvable) toy-model Hamiltonian admitting the asymptotic (i.e., high-excitation) EP-related wave-function degeneracy which, in some sense (i.e., in the limit of large $N$) mimics several aspects of its IEP analogue. In this comparison, the difference is that the regularization of the EP singularities is possible (using an ad hoc perturbation of size ${\cal O}(1/N)$) while an analogous regularization of the IEP singularity is not (we have to consider $N \to \infty$). |
| title | Asymptotic non-Hermitian degeneracy phenomenon and its exactly solvable simulation |
| topic | Quantum Physics Mathematical Physics |
| url | https://arxiv.org/abs/2603.13141 |