{"title":"量子优化传输伪计量学中的增强稳定性：从哈特里到弗拉索夫-泊松","authors":"Mikaela Iacobelli, Laurent Lafleche","doi":"arxiv-2401.05773","DOIUrl":null,"url":null,"abstract":"In this paper we establish almost-optimal stability estimates in quantum\noptimal transport pseudometrics for the semiclassical limit of the Hartree\ndynamics to the Vlasov-Poisson equation, in the regime where the solutions have\nbounded densities. We combine Golse and Paul's method from [Arch. Ration. Mech.\nAnal. 223:57-94, 2017], which uses a semiclassical version of the optimal\ntransport distance and which was adapted to the case of the Coulomb and\ngravitational interactions by the second author in [J. Stat. Phys. 177:20-60,\n2019], with a new approach developed by the first author in [Arch. Ration.\nMech. Anal. 244:27-50, 2022] to quantitatively improve stability estimates in\nkinetic theory.","PeriodicalId":501275,"journal":{"name":"arXiv - PHYS - Mathematical Physics","volume":"51 1","pages":""},"PeriodicalIF":0.0000,"publicationDate":"2024-01-11","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"Enhanced Stability in Quantum Optimal Transport Pseudometrics: From Hartree to Vlasov-Poisson\",\"authors\":\"Mikaela Iacobelli, Laurent Lafleche\",\"doi\":\"arxiv-2401.05773\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"In this paper we establish almost-optimal stability estimates in quantum\\noptimal transport pseudometrics for the semiclassical limit of the Hartree\\ndynamics to the Vlasov-Poisson equation, in the regime where the solutions have\\nbounded densities. We combine Golse and Paul's method from [Arch. Ration. Mech.\\nAnal. 223:57-94, 2017], which uses a semiclassical version of the optimal\\ntransport distance and which was adapted to the case of the Coulomb and\\ngravitational interactions by the second author in [J. Stat. Phys. 177:20-60,\\n2019], with a new approach developed by the first author in [Arch. Ration.\\nMech. Anal. 244:27-50, 2022] to quantitatively improve stability estimates in\\nkinetic theory.\",\"PeriodicalId\":501275,\"journal\":{\"name\":\"arXiv - PHYS - Mathematical Physics\",\"volume\":\"51 1\",\"pages\":\"\"},\"PeriodicalIF\":0.0000,\"publicationDate\":\"2024-01-11\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"arXiv - PHYS - Mathematical Physics\",\"FirstCategoryId\":\"1085\",\"ListUrlMain\":\"https://doi.org/arxiv-2401.05773\",\"RegionNum\":0,\"RegionCategory\":null,\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"\",\"JCRName\":\"\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"arXiv - PHYS - Mathematical Physics","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/arxiv-2401.05773","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
Enhanced Stability in Quantum Optimal Transport Pseudometrics: From Hartree to Vlasov-Poisson
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.
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