A fresh look at the Peierls-Onsager substitution
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arXiv
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| Hauptverfasser: | , , |
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| Format: | Preprint |
| Veröffentlicht: |
2026
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| _version_ | 1866917219576840192 |
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| author | Cornean, Horia D. Helffer, Bernard Purice, Radu |
| author_facet | Cornean, Horia D. Helffer, Bernard Purice, Radu |
| contents | We formulate a general version of the Peierls-Onsager substitution for a finite family of Bloch eigenvalues under a local spectral gap hypothesis, via strongly localized tight-frames and magnetic matrices. This extends the existing results to long-range magnetic fields without any slow-variation hypothesis and without any triviality assumption for the associated Bloch sub-bundle. Moreover, our results cover a large class of periodic, elliptic pseudo-differential operators. We also prove the existence of an approximate time evolution for initial states supported inside the range of the isolated Bloch family, with a precise error control. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2601_16745 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | A fresh look at the Peierls-Onsager substitution Cornean, Horia D. Helffer, Bernard Purice, Radu Mathematical Physics Primary: 81Q10, 81Q15. Secondary: 35S05 We formulate a general version of the Peierls-Onsager substitution for a finite family of Bloch eigenvalues under a local spectral gap hypothesis, via strongly localized tight-frames and magnetic matrices. This extends the existing results to long-range magnetic fields without any slow-variation hypothesis and without any triviality assumption for the associated Bloch sub-bundle. Moreover, our results cover a large class of periodic, elliptic pseudo-differential operators. We also prove the existence of an approximate time evolution for initial states supported inside the range of the isolated Bloch family, with a precise error control. |
| title | A fresh look at the Peierls-Onsager substitution |
| topic | Mathematical Physics Primary: 81Q10, 81Q15. Secondary: 35S05 |
| url | https://arxiv.org/abs/2601.16745 |