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| Main Authors: | , , |
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| Format: | Preprint |
| Published: |
2024
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2408.00009 |
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| _version_ | 1866917778908250112 |
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| author | Dupuy, Mi-Song Letournel, Eloïse Levitt, Antoine |
| author_facet | Dupuy, Mi-Song Letournel, Eloïse Levitt, Antoine |
| contents | We consider the electrons of a molecule in the adiabatic time-dependent density functional theory approximation. We establish the well-posedness of the time evolution and its linear response close to a non-degenerate ground state, and prove the appearance of resonances at relevant frequencies. The main mathematical difficulty is due to the structure of the linearized equations, which are not complex-linear. We bypass this difficulty by reformulating the linearized problem as a real Hamiltonian system, whose stability is ensured by the second-order optimality conditions on the energy. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2408_00009 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Linear response and resonances in adiabatic time-dependent density functional theory Dupuy, Mi-Song Letournel, Eloïse Levitt, Antoine Analysis of PDEs We consider the electrons of a molecule in the adiabatic time-dependent density functional theory approximation. We establish the well-posedness of the time evolution and its linear response close to a non-degenerate ground state, and prove the appearance of resonances at relevant frequencies. The main mathematical difficulty is due to the structure of the linearized equations, which are not complex-linear. We bypass this difficulty by reformulating the linearized problem as a real Hamiltonian system, whose stability is ensured by the second-order optimality conditions on the energy. |
| title | Linear response and resonances in adiabatic time-dependent density functional theory |
| topic | Analysis of PDEs |
| url | https://arxiv.org/abs/2408.00009 |