Enhanced Stability in Quantum Optimal Transport Pseudometrics: From Hartree to Vlasov-Poisson
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arXiv
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| Natura: | Preprint |
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2024
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| _version_ | 1866917850592051200 |
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| author | Iacobelli, Mikaela Lafleche, Laurent |
| author_facet | Iacobelli, Mikaela Lafleche, Laurent |
| contents | In this paper we establish almost-optimal stability estimates in quantum optimal transport pseudometrics for the semiclassical limit of the Hartree dynamics to the Vlasov-Poisson equation, in the regime where the solutions have bounded densities. We combine Golse and Paul's method from [Arch. Ration. Mech. Anal. 223:57-94, 2017], which uses a semiclassical version of the optimal transport distance and which was adapted to the case of the Coulomb and gravitational interactions by the second author in [J. Stat. Phys. 177:20-60, 2019], with a new approach developed by the first author in [Arch. Ration. Mech. Anal. 244:27-50, 2022] to quantitatively improve stability estimates in kinetic theory. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2401_05773 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Enhanced Stability in Quantum Optimal Transport Pseudometrics: From Hartree to Vlasov-Poisson Iacobelli, Mikaela Lafleche, Laurent Analysis of PDEs Mathematical Physics Quantum Physics 81Q20, 81S30, 35Q83, 35Q55 (Primary) 82C10, 49Q22 (Secondary) In this paper we establish almost-optimal stability estimates in quantum optimal transport pseudometrics for the semiclassical limit of the Hartree dynamics to the Vlasov-Poisson equation, in the regime where the solutions have bounded densities. We combine Golse and Paul's method from [Arch. Ration. Mech. Anal. 223:57-94, 2017], which uses a semiclassical version of the optimal transport distance and which was adapted to the case of the Coulomb and gravitational interactions by the second author in [J. Stat. Phys. 177:20-60, 2019], with a new approach developed by the first author in [Arch. Ration. Mech. Anal. 244:27-50, 2022] to quantitatively improve stability estimates in kinetic theory. |
| title | Enhanced Stability in Quantum Optimal Transport Pseudometrics: From Hartree to Vlasov-Poisson |
| topic | Analysis of PDEs Mathematical Physics Quantum Physics 81Q20, 81S30, 35Q83, 35Q55 (Primary) 82C10, 49Q22 (Secondary) |
| url | https://arxiv.org/abs/2401.05773 |