On the Genericity of the Spectrum Intervalization for Multi-Frequency Quasiperiodic Schrödinger Operators
Fuente:
arXiv
Gespeichert in:
| 1. Verfasser: | |
|---|---|
| Format: | Preprint |
| Veröffentlicht: |
2026
|
| Schlagworte: | |
| Online-Zugang: | |
| Tags: |
Tag hinzufügen
Keine Tags, Fügen Sie den ersten Tag hinzu!
|
| _version_ | 1866915982857994240 |
|---|---|
| author | Piao, Daxiong |
| author_facet | Piao, Daxiong |
| contents | This paper proves a genericity conjecture by Goldstein, Schlag, and Voda[Invent. Math.\textbf{217}(2019)] for multi-frequency quasiperiodic Schrödinger operators. Specifically, we show that for almost all coefficients of real trigonometric polynomial potentials, the spectrum forms a single interval under strong coupling conditions. This confirms a long-standing intuition by Chulaevky and Sinai[Comm.Math.Phys.\textbf{125}(1989)] that the spectrum typically intervals for generic potentials, and extends the existence results of Goldstein et al. to a full measure setting. Our proof relies on tools from differential topology, measure theory, and analytic function theory. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2602_07445 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | On the Genericity of the Spectrum Intervalization for Multi-Frequency Quasiperiodic Schrödinger Operators Piao, Daxiong Spectral Theory 47A10, 47B39 This paper proves a genericity conjecture by Goldstein, Schlag, and Voda[Invent. Math.\textbf{217}(2019)] for multi-frequency quasiperiodic Schrödinger operators. Specifically, we show that for almost all coefficients of real trigonometric polynomial potentials, the spectrum forms a single interval under strong coupling conditions. This confirms a long-standing intuition by Chulaevky and Sinai[Comm.Math.Phys.\textbf{125}(1989)] that the spectrum typically intervals for generic potentials, and extends the existence results of Goldstein et al. to a full measure setting. Our proof relies on tools from differential topology, measure theory, and analytic function theory. |
| title | On the Genericity of the Spectrum Intervalization for Multi-Frequency Quasiperiodic Schrödinger Operators |
| topic | Spectral Theory 47A10, 47B39 |
| url | https://arxiv.org/abs/2602.07445 |