By generalizing our automated algebra approach from homogeneous space to harmonically trapped systems, we have calculated the fourth- and fifth-order virial coefficients of universal spin-$\frac{1}{2}$ fermions in the unitary limit, confined in an isotropic harmonic potential. We present results for said coefficients as a function of trapping frequency (or, equivalently, temperature), which compare favorably with previous Monte Carlo calculations (available only at fourth order) as well as with our previous estimates in the untrapped limit (high temperature, low frequency). In addition to the conventional coefficients, we provide estimates for the contributions from subspaces with varying polarization. We use our results for the virial coefficients, together with resummation techniques, to calculate the compressibility and spin susceptibility.

中文翻译：

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调和俘获费米子的四阶和五阶维里膨胀幺正性

通过将我们的自动代数方法从齐次空间推广到谐波捕获系统，我们计算了通用自旋的四阶和五阶维里系数$\frac{1}{2}$单一极限中的费米子，限制在各向同性谐波势中。我们将所述系数的结果呈现为俘获频率（或等效地，温度）的函数，与之前的蒙特卡罗计算（仅在四阶可用）以及我们之前在未俘获极限（高温、低频）。除了常规系数之外，我们还提供了对具有不同极化的子空间的贡献的估计。我们使用我们的维里系数结果以及求和技术来计算可压缩性和自旋敏感性。