Abstract

In recent years, many intriguing physical phenomena associated with quasiperiodic systems have been discovered. However, accurately simulating quasiperiodic systems remains challenging due to their space-filling order without decay or translational invariance. Especially when dealing with wave localization in quasiperiodic quantum systems, existing algorithms may incur an unaffordable computational cost. In this talk, we will propose a new numerical method for quasiperiodic systems, the irrational-window-filter projection method (IWFPM) based on our previously developed projection method. The IWFPM utilizes the concentrated distribution of Fourier coefficients to filter out relevant spectral points using an irrational window. Moreover, an index-shift transform is designed to make the FFT available. The corresponding error analysis on the function approximation level is also given. Then we apply IWFPM to 1D, 2D, and 3D quasiperiodic Schrödinger eigenproblems, demonstrating its accuracy and efficiency. Particularly when addressing localized quantum states, IWFPM exhibits a significant computational advantage.