Holder Continuity of the Spectra for Aperiodic Hamiltonians
- We study the spectral location of a strongly pattern equivariant Hamiltonians arising through configurations on a colored lattice. Roughly speaking, two configurations are "close to each other" if, up to a translation, they "almost coincide" on a large fixed ball. The larger this ball, the more similar they are, and this induces a metric on the space of the corresponding dynamical systems. Our main result states that the map which sends a given configuration into the spectrum of its associated Hamiltonian, is Holder (even Lipschitz) continuous in the usual Hausdorff metric. Specifically, the spectral distance of two Hamiltonians is estimated by the distance of the corresponding dynamical systems.
| Author details: | Siegfried BeckusORCiDGND, Jean BellissardORCiDGND, Horia CorneanORCiDGND |
|---|---|
| DOI: | https://doi.org/10.1007/s00023-019-00848-6 |
| ISSN: | 1424-0637 |
| ISSN: | 1424-0661 |
| Title of parent work (English): | Annales de l'Institut Henri Poincaré |
| Publisher: | Springer |
| Place of publishing: | Cham |
| Publication type: | Article |
| Language: | English |
| Date of first publication: | 2019/09/27 |
| Publication year: | 2019 |
| Release date: | 2020/10/20 |
| Volume: | 20 |
| Issue: | 11 |
| Number of pages: | 29 |
| First page: | 3603 |
| Last Page: | 3631 |
| Organizational units: | Mathematisch-Naturwissenschaftliche Fakultät / Institut für Mathematik |
| DDC classification: | 5 Naturwissenschaften und Mathematik / 51 Mathematik / 510 Mathematik |
| Peer review: | Referiert |
| Publishing method: | Open Access |
| Open Access / Green Open-Access |
