Gespeichert in:
| Hauptverfasser: | , |
|---|---|
| Format: | Preprint |
| Veröffentlicht: |
2024
|
| Schlagworte: | |
| Online-Zugang: | https://arxiv.org/abs/2411.01335 |
| Tags: |
Tag hinzufügen
Keine Tags, Fügen Sie den ersten Tag hinzu!
|
| _version_ | 1866909376132939776 |
|---|---|
| author | Miranda, Pablo Parra, Daniel |
| author_facet | Miranda, Pablo Parra, Daniel |
| contents | We provide eigenvalue asymptotics for a Dirac-type operator on $\mathbb Z^n$, $n\geq 2$, perturbed by multiplication operators that decay as $|μ|^{-γ}$ with $γ<n$. We show that the eigenvalues accumulate near the value of the flat band at a ''semiclassical'' rate with a constant that encodes the structure of the flat band. Similarly, we show that this behaviour can be obtained also for a Laplace operator on a periodic graph. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2411_01335 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Eigenvalue Asymptotics near a flat band in presence of a slowly decaying potential Miranda, Pablo Parra, Daniel Spectral Theory We provide eigenvalue asymptotics for a Dirac-type operator on $\mathbb Z^n$, $n\geq 2$, perturbed by multiplication operators that decay as $|μ|^{-γ}$ with $γ<n$. We show that the eigenvalues accumulate near the value of the flat band at a ''semiclassical'' rate with a constant that encodes the structure of the flat band. Similarly, we show that this behaviour can be obtained also for a Laplace operator on a periodic graph. |
| title | Eigenvalue Asymptotics near a flat band in presence of a slowly decaying potential |
| topic | Spectral Theory |
| url | https://arxiv.org/abs/2411.01335 |