AI 中文总结
研究弱相互作用自旋1/2费米气体中密度的三点等时关联，精确计算总密度三点关联至\({\cal I}\)一阶，还计算了长波长共线极限下同自旋三点关联函数的\({\cal O}({\cal I}^3)\)修正，结果与原子费米气体实验直接相关。
AI 中文摘要
我们研究了弱相互作用自旋1/2费米气体中密度的三点等时关联，并给出了两个新结果。首先，我们精确计算了总密度\(\rho = \rho_\uparrow + \rho_\downarrow\)的三点关联作为动量的函数，精确到无量纲相互作用参数\({\cal I}\)的一阶。这推广了之前将三点函数与朗道费米液体参数\(F_0^s\)和\(F_0^a\)相关联并应用于特定长波长共线极限的结果。其次，我们计算了长波长共线极限下同自旋三点关联函数的主导阶\({\cal O}({\cal I}^3)\)相互作用修正。这些结果与目前使用量子气体显微镜对原子费米气体的实验直接相关。
英文摘要
We study the three-point equal-time correlations of the density in a weakly interacting spin 1/2 Fermi gas and present two new results. First, we compute the three-point correlation for the total density $ρ= ρ_\uparrow + ρ_\downarrow$ exactly as a function of momentum to first order in a dimensionless interaction parameter ${\cal I}$. This generalizes a previous result that related the three-point function to the Landau Fermi liquid parameters $F_0^s$ and $F_0^a$ and applied in a certain long-wavelength collinear limit. Second, we compute the leading order ${\cal O}({\cal I}^3)$ interaction correction to the same-spin three-point correlation function in the long-wavelength collinear limit. These results are directly relevant to current experiments on atomic Fermi gases using quantum gas microscopy.
Comments13 pages, 7 figures, final version
Journal refPhys. Rev. B 114, 105133 (2026)
