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

Bryn Davies; Clemens Thalhammer

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arXiv · 2411.15906

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

Bryn Davies·Clemens Thalhammer

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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 Schr\"odinger and Helmholtz operators.

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BibTeX RIS

Bryn Davies, Clemens Thalhammer. 2024-11-24. Convergence of supercell and superspace methods for computing spectra of quasiperiodic operators. https://arxiv.org/abs/2411.15906

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