Large-order perturbation theory of linear eigenvalue problems
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arXiv
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| Format: | Preprint |
| Published: |
2025
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| _version_ | 1866917244933505024 |
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| author | Chapman, Stephen Jonathan |
| author_facet | Chapman, Stephen Jonathan |
| contents | We consider a class of linear eigenvalue problems depending on a small parameter epsilon in which the series expansion for the eigenvalue in powers of epsilon is divergent. We develop a new technique to determine the precise nature of this divergence. We illustrate the technique through its application to four examples: the anharmonic oscillator, a simplified model of equatorially-trapped Rossby waves, and two simplified models based on quasinormal modes of Reissner-Nordstrom-de Sitter black holes. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2509_14763 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Large-order perturbation theory of linear eigenvalue problems Chapman, Stephen Jonathan Classical Analysis and ODEs General Relativity and Quantum Cosmology Quantum Physics 34E05 (Primary), 34E15, 34E20, 81-10 (Secondary) We consider a class of linear eigenvalue problems depending on a small parameter epsilon in which the series expansion for the eigenvalue in powers of epsilon is divergent. We develop a new technique to determine the precise nature of this divergence. We illustrate the technique through its application to four examples: the anharmonic oscillator, a simplified model of equatorially-trapped Rossby waves, and two simplified models based on quasinormal modes of Reissner-Nordstrom-de Sitter black holes. |
| title | Large-order perturbation theory of linear eigenvalue problems |
| topic | Classical Analysis and ODEs General Relativity and Quantum Cosmology Quantum Physics 34E05 (Primary), 34E15, 34E20, 81-10 (Secondary) |
| url | https://arxiv.org/abs/2509.14763 |