论文标题
全球统一$ n $估计的hartree-fock-bogoliubov类型的解决方案的估计值$β<1 $
Global uniform in $N$ estimates for solutions of a system of Hartree-Fock-Bogoliubov type in the case $β<1$
论文作者
论文摘要
我们将2019年论文的结果扩展到全球第三和第四作者。更准确地说，我们证明了解决方案的$ n $估计值$ ϕ $，$λ$和$γ$的Hartree-fock-Bogoliubov类型的耦合系统，具有相互作用的潜在$ v_n（x-y）= n^{3β} v（n^β（x-yβ（x-y）$）与$ ubb <1 $ $ bebe。潜力满足某些技术条件，但并不小。初始条件具有有限的能量，“配对相关”部分满足了较小的条件，但否则是合适的Sobolev空间中的一般功能，$λ$的预期相关性随着时间的推移动态发展。预计估计将提高第一和第五作者的2021年论文的Fock空间界限。这将在不同的论文中解决。
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 $V_N(x-y)=N^{3 β}v(N^β(x-y))$ 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.
