Global well-posedness of the nonlinear Hartree equation for infinitely many particles with singular interaction
Fuente:
arXiv
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| Autori principali: | , |
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| Natura: | Preprint |
| Pubblicazione: |
2024
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| _version_ | 1866915724378767360 |
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| author | Hadama, Sonae Hong, Younghun |
| author_facet | Hadama, Sonae Hong, Younghun |
| contents | The nonlinear Hartree equation (NLH) in the Heisenberg picture admits steady states of the form $γ_f=f(-Δ)$ representing quantum states of infinitely many particles. In this article, we consider the time evolution of perturbations from a large class of such steady states via the three-dimensional NLH. We prove that if the interaction potential $w$ has finite measure and initial states have finite relative entropy, then solutions preserve the relative free energy, and they exist globally in time. This result extends the important work of Lewin and Sabin [arXiv:1310.0603] to singular interaction cases. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2404_06730 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Global well-posedness of the nonlinear Hartree equation for infinitely many particles with singular interaction Hadama, Sonae Hong, Younghun Analysis of PDEs Mathematical Physics The nonlinear Hartree equation (NLH) in the Heisenberg picture admits steady states of the form $γ_f=f(-Δ)$ representing quantum states of infinitely many particles. In this article, we consider the time evolution of perturbations from a large class of such steady states via the three-dimensional NLH. We prove that if the interaction potential $w$ has finite measure and initial states have finite relative entropy, then solutions preserve the relative free energy, and they exist globally in time. This result extends the important work of Lewin and Sabin [arXiv:1310.0603] to singular interaction cases. |
| title | Global well-posedness of the nonlinear Hartree equation for infinitely many particles with singular interaction |
| topic | Analysis of PDEs Mathematical Physics |
| url | https://arxiv.org/abs/2404.06730 |