论文标题
通过Bogoliubov理论稀释的费米气体
The dilute Fermi gas via Bogoliubov theory
论文作者
论文摘要
我们研究了三个维度，研究稀释状态中相互作用的费米气体的基态特性。我们计算系统的基态能量，以获得正相互作用的势。我们在粒子密度下以二阶为基态能量恢复了一个众所周知的表达，这仅取决于相互作用的散射长度。 Lieb，Seiringer和Solovej给出了这一结果的第一个证明。在本文中，我们使用不同的方法给出了该公式的新推导。它的灵感来自Bogoliubov理论，并利用了系统低能激发的几乎骨质性质。关于以前的工作，我们的结果适用于更常规的相互作用电位，但它在密度下对基态能量渐近性的误差估计得到了改善。
We study the ground state properties of interacting Fermi gases in the dilute regime, in three dimensions. We compute the ground state energy of the system, for positive interaction potentials. We recover a well-known expression for the ground state energy at second order in the particle density, which depends on the interaction potential only via its scattering length. The first proof of this result has been given by Lieb, Seiringer and Solovej. In this paper we give a new derivation of this formula, using a different method; it is inspired by Bogoliubov theory, and it makes use of the almost-bosonic nature of the low-energy excitations of the systems. With respect to previous work, our result applies to a more regular class of interaction potentials, but it comes with improved error estimates on the ground state energy asymptotics in the density.
