Gespeichert in:
| Hauptverfasser: | , |
|---|---|
| Format: | Preprint |
| Veröffentlicht: |
2023
|
| Schlagworte: | |
| Online-Zugang: | https://arxiv.org/abs/2306.08248 |
| Tags: |
Tag hinzufügen
Keine Tags, Fügen Sie den ersten Tag hinzu!
|
| _version_ | 1866918116201594880 |
|---|---|
| author | Petermann, Eric Hinrichsen, Haye |
| author_facet | Petermann, Eric Hinrichsen, Haye |
| contents | We examine a specific category of eigenfunctions of the lattice Laplacian on $\{p,q\}$-tessellations of the Poincaré disk that bear resemblance to plane waves in the continuum case. Our investigation reveals that the lattice eigenmodes deviate from the continuum solutions by a factor that depends solely on the local inclination of the vertex in relation to the wave's propagation direction. This allows us to compute certain eigenfunctions by numerical and analytical methods. For various special cases we find explicit exact eigenfunctions and their eigenvalues on the infinite lattice. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2306_08248 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Eigenmodes of the Laplacian on Hyperbolic Lattices Petermann, Eric Hinrichsen, Haye Other Condensed Matter General Relativity and Quantum Cosmology We examine a specific category of eigenfunctions of the lattice Laplacian on $\{p,q\}$-tessellations of the Poincaré disk that bear resemblance to plane waves in the continuum case. Our investigation reveals that the lattice eigenmodes deviate from the continuum solutions by a factor that depends solely on the local inclination of the vertex in relation to the wave's propagation direction. This allows us to compute certain eigenfunctions by numerical and analytical methods. For various special cases we find explicit exact eigenfunctions and their eigenvalues on the infinite lattice. |
| title | Eigenmodes of the Laplacian on Hyperbolic Lattices |
| topic | Other Condensed Matter General Relativity and Quantum Cosmology |
| url | https://arxiv.org/abs/2306.08248 |