Convergence of supercell and superspace methods for computing spectra of quasiperiodic operators
Fuente:
arXiv
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| Autores principales: | , |
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| Formato: | Preprint |
| Publicado: |
2024
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| _version_ | 1866916494101708800 |
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| author | Davies, Bryn Thalhammer, Clemens |
| author_facet | Davies, Bryn Thalhammer, Clemens |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2411_15906 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Convergence of supercell and superspace methods for computing spectra of quasiperiodic operators Davies, Bryn Thalhammer, Clemens Spectral Theory Mathematical Physics Analysis of PDEs 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. |
| title | Convergence of supercell and superspace methods for computing spectra of quasiperiodic operators |
| topic | Spectral Theory Mathematical Physics Analysis of PDEs |
| url | https://arxiv.org/abs/2411.15906 |