The Dry Ten Martini Problem for Sturmian Hamiltonians
Fuente:
arXiv
Guardado en:
| Autores principales: | , , |
|---|---|
| Formato: | Preprint |
| Publicado: |
2024
|
| Materias: | |
| Acceso en línea: | |
| Etiquetas: |
Agregar Etiqueta
Sin Etiquetas, Sea el primero en etiquetar este registro!
|
| _version_ | 1866916138836819968 |
|---|---|
| author | Band, Ram Beckus, Siegfried Loewy, Raphael |
| author_facet | Band, Ram Beckus, Siegfried Loewy, Raphael |
| contents | The Dry Ten Martini Problem for Sturmian Hamiltonians is affirmatively solved. Concretely, we prove that all spectral gaps are open for Schrödinger operators with Sturmian potentials and non-vanishing coupling constant. A key approach towards the solution is a representation of the spectrum as the boundary of an infinite tree. This tree is constructed via particular periodic approximations and it encodes substantial spectral characteristics. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2402_16703 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | The Dry Ten Martini Problem for Sturmian Hamiltonians Band, Ram Beckus, Siegfried Loewy, Raphael Mathematical Physics Spectral Theory The Dry Ten Martini Problem for Sturmian Hamiltonians is affirmatively solved. Concretely, we prove that all spectral gaps are open for Schrödinger operators with Sturmian potentials and non-vanishing coupling constant. A key approach towards the solution is a representation of the spectrum as the boundary of an infinite tree. This tree is constructed via particular periodic approximations and it encodes substantial spectral characteristics. |
| title | The Dry Ten Martini Problem for Sturmian Hamiltonians |
| topic | Mathematical Physics Spectral Theory |
| url | https://arxiv.org/abs/2402.16703 |