Efficient Numerical Method for Solving Arbitrary Dimensional Quasiperiodic Schrödinger Eigenproblems

The paper proposes a new algorithm, the irrational-window-filter projection method (IWFPM), for efficiently solving arbitrary dimensional global quasiperiodic systems, especially quasiperiodic Schrödinger eigenproblems. IWFPM utilizes the concentrated distribution of Fourier coefficients to filter out relevant spectral points using an irrational window and employs an index-shift transform to enable the use of Fast Fourier Transform.