On the asymptotic behavior of the spectral gap for discrete Schrödinger operators
Fuente:
arXiv
Gespeichert in:
| Hauptverfasser: | , , |
|---|---|
| Format: | Preprint |
| Veröffentlicht: |
2025
|
| Schlagworte: | |
| Online-Zugang: | |
| Tags: |
Tag hinzufügen
Keine Tags, Fügen Sie den ersten Tag hinzu!
|
| _version_ | 1866912811842535424 |
|---|---|
| author | Hofmann, Matthias Kerner, Joachim Pechmann, Maximilian |
| author_facet | Hofmann, Matthias Kerner, Joachim Pechmann, Maximilian |
| contents | In this note we elaborate on the asymptotic behavior of the spectral gap of a class of discrete Schrödinger operators defined on a path graph in the limit of infinite volume. We confirm recent results and generalize them to a larger class of potentials using entirely different methods. Notably, we also resolve a conjecture previously proposed in this context. This then yields new insights into the rate at which the spectral gap tends to zero as the volume increases. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2508_16353 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | On the asymptotic behavior of the spectral gap for discrete Schrödinger operators Hofmann, Matthias Kerner, Joachim Pechmann, Maximilian Spectral Theory Mathematical Physics 05C38, 15A18, 47N50, 47B93 In this note we elaborate on the asymptotic behavior of the spectral gap of a class of discrete Schrödinger operators defined on a path graph in the limit of infinite volume. We confirm recent results and generalize them to a larger class of potentials using entirely different methods. Notably, we also resolve a conjecture previously proposed in this context. This then yields new insights into the rate at which the spectral gap tends to zero as the volume increases. |
| title | On the asymptotic behavior of the spectral gap for discrete Schrödinger operators |
| topic | Spectral Theory Mathematical Physics 05C38, 15A18, 47N50, 47B93 |
| url | https://arxiv.org/abs/2508.16353 |