Construction of maximally non-Hermitian potentials under unbroken PT-symmetry constraint
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arXiv
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| Format: | Preprint |
| Publié: |
2025
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| _version_ | 1866916893649010688 |
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| author | Znojil, Miloslav |
| author_facet | Znojil, Miloslav |
| contents | A family of discrete Schrödinger equations with imaginary potentials $V(x)$ is studied. Inside the domain ${\cal D}$ of unitarity-compatible values of $V(x)$, the reality of all of the bound-state energies survives up to the ``exceptional-point'' (EP) maximally non-Hermitian spectral-degeneracy boundaries $\partial {\cal D}$. The computer-assisted localization of the EP limits is performed showing that the complexity of the task grows quickly with the number $N$ of grid points $x$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2507_09567 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Construction of maximally non-Hermitian potentials under unbroken PT-symmetry constraint Znojil, Miloslav Mathematical Physics Algebraic Geometry Quantum Physics A family of discrete Schrödinger equations with imaginary potentials $V(x)$ is studied. Inside the domain ${\cal D}$ of unitarity-compatible values of $V(x)$, the reality of all of the bound-state energies survives up to the ``exceptional-point'' (EP) maximally non-Hermitian spectral-degeneracy boundaries $\partial {\cal D}$. The computer-assisted localization of the EP limits is performed showing that the complexity of the task grows quickly with the number $N$ of grid points $x$. |
| title | Construction of maximally non-Hermitian potentials under unbroken PT-symmetry constraint |
| topic | Mathematical Physics Algebraic Geometry Quantum Physics |
| url | https://arxiv.org/abs/2507.09567 |