Scattering for the one dimensional Hartree Fock equation
Fuente:
arXiv
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| Autore principale: | |
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| Natura: | Preprint |
| Pubblicazione: |
2024
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| _version_ | 1866909532094988288 |
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| author | Malézé, Cyril |
| author_facet | Malézé, Cyril |
| contents | We consider the Hartree-Fock equation in 1D, for a small and localised initial data and a finite measure potential. We show that there is no long range scattering due to a nonlinear cancellation between the direct term and the exchange term for plane waves. We employ the framework of space-time resonances that enables us to single out precisely this cancellation and to obtain scattering to linear waves as a consequence. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2406_17715 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Scattering for the one dimensional Hartree Fock equation Malézé, Cyril Analysis of PDEs We consider the Hartree-Fock equation in 1D, for a small and localised initial data and a finite measure potential. We show that there is no long range scattering due to a nonlinear cancellation between the direct term and the exchange term for plane waves. We employ the framework of space-time resonances that enables us to single out precisely this cancellation and to obtain scattering to linear waves as a consequence. |
| title | Scattering for the one dimensional Hartree Fock equation |
| topic | Analysis of PDEs |
| url | https://arxiv.org/abs/2406.17715 |