用Bogoliubov理论研究稀费米气体
The dilute Fermi gas via Bogoliubov theory
摘要：
本文研究了在三维空间中相互作用的费米气体在稀态下的基态性质。我们计算了系统的基态能量，对于正的相互作用势。我们恢复了一个众所周知的表达式的基态能量在第二阶的粒子密度，这取决于相互作用势仅通过其散射长度。这个结果的第一个证明已经由Lieb，Seiringer和Solovej给出。在本文中，我们给出了这个公式的一个新的推导，使用不同的方法，它的灵感来自Bogoliubov理论，它利用了系统的低能量激发的几乎玻色子性质。相对于以前的工作，我们的结果适用于一个更经常的相互作用势类，但它带来了改进的误差估计的基态能量渐近密度。
英文摘要：
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.
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