论文标题
在三维中稀释的费米气体的最佳上限
An optimal upper bound for the dilute Fermi gas in three dimensions
论文作者
论文摘要
在相互作用的费米子系统中，相关能量被定义为基态能量与自由费米气体之一之间的差异。我们认为$ n $互动的旋转$ 1/2 $ fermions在稀释状态下，即$ρ\ ll 1 $，其中$ρ$是系统的总密度。我们严格地在热力学限制中以$ \ mathcal {o}（ρ^{7/3}）$的最佳误差项为相关能量提供了一阶的上限。此外，我们相对于先前的结果提高了下限估计，获得了错误$ \ MATHCAL {O}（ρ^{2+1/5}）$。
In a system of interacting fermions, the correlation energy is defined as the difference between the energy of the ground state and the one of the free Fermi gas. We consider $N$ interacting spin $1/2$ fermions in the dilute regime, i.e., $ρ\ll 1$ where $ρ$ is the total density of the system. We rigorously derive a first order upper bound for the correlation energy with an optimal error term of the order $\mathcal{O}(ρ^{7/3})$ in the thermodynamic limit. Moreover, we improve the lower bound estimate with respect to previous results getting an error $\mathcal{O}(ρ^{2+1/5})$.
