Spectral Regularity and Defects for the Kohmoto Model
Abstract We study the Kohmoto model including Sturmian Hamiltonians and the associated Kohmoto butterfly. We prove spectral estimates for the operators using Farey numbers. In addition, we determine the impurities at rational rotations leading to the spectral defects in the Kohmoto butterfly. Our results are similar to the ones obtained for the almost-Mathieu operator and the associated Hofstadter butterfly.
Authors
- Siegfried Beckus (ORCID: https://orcid.org/0000-0003-0724-9258)
- Jean Bellissard (ORCID: https://orcid.org/0000-0002-3766-7365)
- Y. Thomas
Institutions
- Georgia Institute of Technology (US)
- University of Potsdam (DE)
- Mathematical Research Institute of Oberwolfach (DE)
Publication Details
- Journal
- Annales Henri Poincaré
- Published
- 2025-05-10
- DOI
- https://doi.org/10.1007/s00023-025-01578-8
- Primary Topic
- Spectral Theory in Mathematical Physics
- Type
- article
- Field-Weighted Citation Impact
- 0.00
Funders
- Deutsche Forschungsgemeinschaft
- Mathematisches Forschungsinstitut Oberwolfach