Irrational-Window-Filter Projection Method and Application to Quasiperiodic Schrödinger Eigenproblems

IF 2.8 2区数学 Q1 MATHEMATICS, APPLIED

SIAM Journal on Numerical Analysis Pub Date : 2025-03-11 DOI:10.1137/24m1666197

Kai Jiang, Xueyang Li, Yao Ma, Juan Zhang, Pingwen Zhang, Qi Zhou

引用次数: 0

Abstract

SIAM Journal on Numerical Analysis, Volume 63, Issue 2, Page 564-587, April 2025.
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 one-dimensional, two-dimensional (2D), and three-dimensional (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.

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无理性窗滤波投影法及其在拟周期Schrödinger特征问题中的应用

SIAM数值分析杂志，第63卷，第2期，第564-587页，2025年4月。摘要。本文针对具有集中谱点分布的准周期系统，提出了一种新的算法——无理性窗滤波投影法。基于投影法（PM）， IWFPM通过定义一个非理性窗口来滤除优势谱点，并使用相应的指数移位变换使FFT可用。给出了函数逼近级的误差分析。我们将IWFPM应用于一维，二维（2D）和三维（3D）准周期Schrödinger特征问题（qse），以证明其准确性和效率。IWFPM在扩展和局域量子态方面都比PM具有显著的计算优势。更重要的是，通过IWFPM，数值验证了二维和三维qse中Anderson定位的存在性。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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来源期刊

SIAM Journal on Numerical Analysis 数学-应用数学

CiteScore

4.80

自引率

6.90%

发文量

110

审稿时长

4-8 weeks

期刊介绍： SIAM Journal on Numerical Analysis (SINUM) contains research articles on the development and analysis of numerical methods. Topics include the rigorous study of convergence of algorithms, their accuracy, their stability, and their computational complexity. Also included are results in mathematical analysis that contribute to algorithm analysis, and computational results that demonstrate algorithm behavior and applicability.