Irrational-window-filter projection method and application to quasiperiodic Schrödinger eigenproblems
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arXiv
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| Autori principali: | , , , , , |
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| Natura: | Preprint |
| Pubblicazione: |
2024
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| _version_ | 1866910707683950592 |
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| author | Jiang, Kai Li, Xueyang Ma, Yao Zhang, Juan Zhang, Pingwen Zhou, Qi |
| author_facet | Jiang, Kai Li, Xueyang Ma, Yao Zhang, Juan Zhang, Pingwen Zhou, Qi |
| contents | In this paper, we propose a new algorithm, the irrational-window-filter projection method (IWFPM), for quasiperiodic systems with concentrated spectral point distribution. Based on the projection method (PM), IWFPM filters out dominant spectral points by defining an irrational window and uses a corresponding index-shift transform to make the FFT available. The error analysis on the function approximation level is also given. We apply IWFPM to 1D, 2D, and 3D quasiperiodic Schrödinger eigenproblems (QSEs) to demonstrate its accuracy and efficiency. IWFPM exhibits a significant computational advantage over PM for both extended and localized quantum states. More importantly, by using IWFPM, the existence of Anderson localization in 2D and 3D QSEs is numerically verified. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2404_04507 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Irrational-window-filter projection method and application to quasiperiodic Schrödinger eigenproblems Jiang, Kai Li, Xueyang Ma, Yao Zhang, Juan Zhang, Pingwen Zhou, Qi Numerical Analysis 35P05, 35J10, 65D15, 65T50, 81-08 In this paper, we propose a new algorithm, the irrational-window-filter projection method (IWFPM), for quasiperiodic systems with concentrated spectral point distribution. Based on the projection method (PM), IWFPM filters out dominant spectral points by defining an irrational window and uses a corresponding index-shift transform to make the FFT available. The error analysis on the function approximation level is also given. We apply IWFPM to 1D, 2D, and 3D quasiperiodic Schrödinger eigenproblems (QSEs) to demonstrate its accuracy and efficiency. IWFPM exhibits a significant computational advantage over PM for both extended and localized quantum states. More importantly, by using IWFPM, the existence of Anderson localization in 2D and 3D QSEs is numerically verified. |
| title | Irrational-window-filter projection method and application to quasiperiodic Schrödinger eigenproblems |
| topic | Numerical Analysis 35P05, 35J10, 65D15, 65T50, 81-08 |
| url | https://arxiv.org/abs/2404.04507 |