标题： 黄-杨公式用于低密度费米气体：上界 显示英文标题

标题： The Huang-Yang formula for the low-density Fermi gas: upper bound

摘要： 我们研究具有排斥短程相互作用的自旋$1/2$费米子气体的基态能量。 我们推导出一个上界，在低密度$\rho$时与黄-杨猜想一致。 后者捕捉了低密度渐近展开中的前三项，特别是阶数为$\rho^{7/3}$的黄-杨修正项。 我们的试验态是通过将玻色子 Bogoliubov 理论适应到费米系统中构造的，其中费米子粒子的相关结构通过准玻色子 Bogoliubov 变换来体现。 在后者中，重要的是要考虑一个修改后的零能散射方程，该方程考虑到费米海的存在，这与 Bethe-Goldstone 方程的精神一致。 显示英文摘要

摘要： We study the ground state energy of a gas of spin $1/2$ fermions with repulsive short-range interactions. We derive an upper bound that agrees, at low density $\rho$, with the Huang-Yang conjecture. The latter captures the first three terms in an asymptotic low-density expansion, and in particular the Huang-Yang correction term of order $\rho^{7/3}$. Our trial state is constructed using an adaptation of the bosonic Bogoliubov theory to the Fermi system, where the correlation structure of fermionic particles is incorporated by quasi-bosonic Bogoliubov transformations. In the latter, it is important to consider a modified zero-energy scattering equation that takes into account the presence of the Fermi sea, in the spirit of the Bethe-Goldstone equation.