Limit absorption and Green function estimates for matrix-valued periodic operators
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arXiv
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| Auteurs principaux: | , , |
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| Format: | Preprint |
| Publié: |
2025
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| _version_ | 1866909950957060096 |
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| author | Ballesteros, Miguel Cordova, Gerardo Franco Schulz-Baldes, Hermann |
| author_facet | Ballesteros, Miguel Cordova, Gerardo Franco Schulz-Baldes, Hermann |
| contents | The boundary value of the resolvent of a generic periodic tight-binding Hamiltonian with matrix symbols is shown to satisfy a limit absorption principle which is continuous in energy in dimensions $d=3$, and in dimension $d=2$ away from critical points of the energy bands corresponding to van Hove singularities. The analysis away from critical points of the energy bands is based on the coarea formula, while at the critical points it involves a parametric Morse lemma and stationary phase arguments. In particular, at Weyl points a new type of oscillatory integrals is dealt with. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2512_08335 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Limit absorption and Green function estimates for matrix-valued periodic operators Ballesteros, Miguel Cordova, Gerardo Franco Schulz-Baldes, Hermann Mathematical Physics The boundary value of the resolvent of a generic periodic tight-binding Hamiltonian with matrix symbols is shown to satisfy a limit absorption principle which is continuous in energy in dimensions $d=3$, and in dimension $d=2$ away from critical points of the energy bands corresponding to van Hove singularities. The analysis away from critical points of the energy bands is based on the coarea formula, while at the critical points it involves a parametric Morse lemma and stationary phase arguments. In particular, at Weyl points a new type of oscillatory integrals is dealt with. |
| title | Limit absorption and Green function estimates for matrix-valued periodic operators |
| topic | Mathematical Physics |
| url | https://arxiv.org/abs/2512.08335 |