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The Dilute Fermi Gas via Bogoliubov Theory
Annales Henri Poincaré ( IF 1.5 ) Pub Date : 2021-04-16 , DOI: 10.1007/s00023-021-01031-6
Marco Falconi 1 , Emanuela L Giacomelli 2 , Christian Hainzl 2 , Marcello Porta 3
Affiliation  

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 (Phys Rev A 71:053605, 2005). 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.



中文翻译:

通过 Bogoliubov 理论稀释费米气体

我们从三个维度研究了稀释状态下相互作用的费米气体的基态特性。对于正相互作用势,我们计算系统的基态能量。我们恢复了粒子密度二阶基态能量的众所周知的表达式,它仅通过其散射长度取决于相互作用势。Lieb、Seiringer 和 Solovej (Phys Rev A 71:053605, 2005) 给出了该结果的第一个证明。在本文中,我们使用不同的方法对这个公式进行了新的推导;它的灵感来自 Bogoliubov 理论,它利用了系统低能激发的几乎玻色子性质。相对于以前的工作,我们的结果适用于更规则的相互作用势类,

更新日期:2021-04-16
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