Convergence of supercell and superspace methods for computing spectra of quasiperiodic operators
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2025-01
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Report
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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 Schrodinger and Helmholtz operators.
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published
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2025-03
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Seminar for Applied Mathematics, ETH Zurich
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Subject
Quasicrystal; Cut and project; Fractal spectrum; Cantor set; Fibonacci tiling; Almost Mathieu operator
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09504 - Ammari, Habib / Ammari, Habib