Schrödinger Operators with Potentials Generated by Hyperbolic Transformations: II. Large Deviations and Anderson Localization
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arXiv
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| Main Authors: | , , |
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| Format: | Preprint |
| Published: |
2024
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| _version_ | 1866911768826085376 |
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| author | Avila, Artur Damanik, David Zhang, Zhenghe |
| author_facet | Avila, Artur Damanik, David Zhang, Zhenghe |
| contents | We consider discrete one-dimensional Schrödinger operators whose potentials are generated by Hölder continuous sampling along the orbits of a uniformly hyperbolic transformation. For any ergodic measure satisfying a suitable bounded distortion property, we establish a uniform large deviation estimate in a large energy region provided that the sampling function is locally constant or has small supremum norm. We also prove full spectral Anderson localization for the operators in question. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2402_00215 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Schrödinger Operators with Potentials Generated by Hyperbolic Transformations: II. Large Deviations and Anderson Localization Avila, Artur Damanik, David Zhang, Zhenghe Spectral Theory Mathematical Physics Dynamical Systems We consider discrete one-dimensional Schrödinger operators whose potentials are generated by Hölder continuous sampling along the orbits of a uniformly hyperbolic transformation. For any ergodic measure satisfying a suitable bounded distortion property, we establish a uniform large deviation estimate in a large energy region provided that the sampling function is locally constant or has small supremum norm. We also prove full spectral Anderson localization for the operators in question. |
| title | Schrödinger Operators with Potentials Generated by Hyperbolic Transformations: II. Large Deviations and Anderson Localization |
| topic | Spectral Theory Mathematical Physics Dynamical Systems |
| url | https://arxiv.org/abs/2402.00215 |