2022/03/10 by Jacky J. Chong, Jacky Chong, Chong, Jacky +8
Mathematics · #Advanced Mathematical Physics Problems #Analysis of PDEs (math.AP) #Differential Equations and Boundary Problems #FOS: Mathematics #Spectral Theory in Mathematical Physics #math.AP
paper · pdf · doi:10.48550/arxiv.2203.05447
53 pages. Comments are welcome!
arxiv created 2022/03/10 · openalex publication_date 2022/03/10 · arxiv updated 2022/03/11 · openalex created_date 2022/05/05 · openalex updated_date 2026/07/28
We extend the results of the 2019 paper by the third and fourth author globally in time. More precisely, we prove uniform in N estimates for the solutions ϕ, Λ and Γ of a coupled system of Hartree-Fock-Bogoliubov type with interaction potential VN(x-y)=N3 βv(Nβ(x-y)) with β<1. The potential satisfies some technical conditions, but is not small. The initial conditions have finite energy and the "pair correlation" part satisfies a smallness condition, but are otherwise general functions in suitable Sobolev spaces, and the expected correlations in Λ develop dynamically in time. The estimates are expected to improve the Fock space bounds from the 2021 paper of the first and fifth author. This will be addressed in a different paper.