[2404.04507] Irrational-window-filter projection method and application to quasiperiodic Schrödinger eigenproblems
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Mathematics > Numerical Analysis

arXiv:2404.04507 (math)
[Submitted on 6 Apr 2024 (v1), last revised 22 Nov 2024 (this version, v4)]

Title:Irrational-window-filter projection method and application to quasiperiodic Schrödinger eigenproblems

Authors:Kai Jiang, Xueyang Li, Yao Ma, Juan Zhang, Pingwen Zhang, Qi Zhou
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Abstract: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.
Subjects: Numerical Analysis (math.NA)
MSC classes: 35P05, 35J10, 65D15, 65T50, 81-08
Cite as: arXiv:2404.04507 [math.NA]
  (or arXiv:2404.04507v4 [math.NA] for this version)
  https://doi.org/10.48550/arXiv.2404.04507

Submission history

From: Kai Jiang [view email]
[v1] Sat, 6 Apr 2024 05:27:59 UTC (1,909 KB)
[v2] Fri, 19 Apr 2024 02:05:29 UTC (1,903 KB)
[v3] Sun, 30 Jun 2024 06:32:39 UTC (1,904 KB)
[v4] Fri, 22 Nov 2024 01:25:22 UTC (1,286 KB)
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