Convergence of supercell and superspace methods for computing spectra of quasiperiodic operators

2024/11/24 by Bryn Davies, Davies, Bryn, Clemens Thalhammer +1 · 2 citations
Computer Science · Mathematics · #Analysis of PDEs (math.AP) #Approximation Theory and Sequence Spaces #FOS: Mathematics #FOS: Physical sciences #Iterative Methods for Nonlinear Equations #Mathematical Physics (math-ph) #Matrix Theory and Algorithms #Spectral Theory (math.SP)

paper · pdf · doi:10.48550/arxiv.2411.15906

openalex publication_date 2024/11/24 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We study the convergence of two of the most widely used and intuitive approaches for computing the spectra of differential operators with quasiperiodic coefficients: the supercell method and the superspace method. In both cases, Floquet-Bloch theory for periodic operators can be used to compute approximations to the spectrum. We illustrate our results with examples of Schrödinger and Helmholtz operators.

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• Energy estimates for wave amplification in quasiperiodic Fibonacci time-modulated media

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