AI 中文总结
本文针对散射长度为负或无穷大的均匀费米气体，在非简并极限下计算三体接触$C_3$的领头阶，采用波函数方法和费曼图技术分别处理$a=\infty$与$a<0$的情况，得到了$C_3$的相关解析结果与幂律标度。
AI 中文摘要
具有零程相互作用的费米气体的一个基本特征量是三体接触$C_3$，如姊妹文章所示，它决定了多个可观测量，包括冷原子实验中费米子近邻三体对的数量和三体损失率。本文中，我们针对散射长度$a$为负或无穷大的均匀气体，在非简并极限下计算$C_3$的领头阶。当$a=\infty$时，我们采用波函数方法得到$C_3$的解析表达式，其对温度$T$的依赖关系呈现出极缓慢的$1/T^{0.22728}$形式。对于$a<0$的情况，我们使用费曼图技术，只有在领头阶两体关联和三体关联之间发生非平凡抵消后，才会出现正确的三体短程关联；所得的幂律标度来自三体T矩阵的大波矢尾，我们是在单位极限下三体问题解析解的启发下推导得到该尾的。
英文摘要
A fundamental quantity characterizing Fermi gases with zero-range interactions is the three-body contact $C_3$, which determines several observables including the number of nearby triplets of fermions and the three-body loss rate in cold atom experiments, as shown in a companion article. Here, we compute $C_3$ to leading order in the non-degenerate limit for the homogeneous gas with negative or infinite scattering length $a$. At $a=\infty$, using a wavefunction approach, we obtain the analytical expression of $C_3$, which has a remarkably slow $1/T^{0.22728}$ dependence on the temperature $T$. In the Feynman diagram technique, which we use for $a<0$, the correct three-body short-distance correlations emerge only after a non-trivial cancellation between leading order two-body and three-body correlations, and the resulting power-law scaling comes from the large-wavevector tail of the 3-body T-matrix, which we derive inspired by the analytical solution of the three-body problem at the unitary limit.
