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| Main Authors: | , |
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| Format: | Preprint |
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2025
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| Online Access: | https://arxiv.org/abs/2502.15284 |
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| _version_ | 1866911093467643904 |
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| author | Zhang, Bei Piao, Daxiong |
| author_facet | Zhang, Bei Piao, Daxiong |
| contents | In this paper we prove Anderson localization for multi-frequency quasi-periodic extended CMV matrices with analytic Verblunsky coefficients in the regime of positive Lyapunov exponents. By constructing a suitable semialgebraic set and combining the Avalanche Principle with a Large Deviation Theorem, we overcome the key obstruction of eliminating double resonances along the orbit, where multi-frequency potentials introduce significant challenges compared to the single-frequency case. As a direct application, we establish Anderson localization for corresponding analytic multi-frequency quasi-periodic quantum walks via unitary equivalence. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2502_15284 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Anderson localization for the multi-frequency quasi-periodic CMV matrices and quantum walks Zhang, Bei Piao, Daxiong Spectral Theory 37A30, 42C05, 70G60 In this paper we prove Anderson localization for multi-frequency quasi-periodic extended CMV matrices with analytic Verblunsky coefficients in the regime of positive Lyapunov exponents. By constructing a suitable semialgebraic set and combining the Avalanche Principle with a Large Deviation Theorem, we overcome the key obstruction of eliminating double resonances along the orbit, where multi-frequency potentials introduce significant challenges compared to the single-frequency case. As a direct application, we establish Anderson localization for corresponding analytic multi-frequency quasi-periodic quantum walks via unitary equivalence. |
| title | Anderson localization for the multi-frequency quasi-periodic CMV matrices and quantum walks |
| topic | Spectral Theory 37A30, 42C05, 70G60 |
| url | https://arxiv.org/abs/2502.15284 |