Using a coarse temporal lattice approximation, we calculate the first few terms of the virial expansion of a three-species fermion system with a three-body contact interaction in $d$ spatial dimensions, both in homogeneous space and in a harmonic trapping potential of frequency $\omega$. Using the three-body problem to renormalize, we report analytic results for the change in the fourth- and fifth-order virial coefficients $\mathrm{\Delta }{b}_4$ and $\mathrm{\Delta }{b}_5$ as functions of $\mathrm{\Delta }{b}_3$. Additionally, we argue that in the $\omega \to 0$ limit the relationship $b_n^{\text{T}}=n^{-d/2}{b}_n$ holds between the trapped (T) and the homogeneous coefficients for arbitrary temperature and coupling strength (not merely in scale-invariant regimes). Finally, we point out an exact, universal (coupling- and frequency-independent) relationship between $\mathrm{\Delta }{b}_3^{\text{T}}$ in one dimension with three-body forces and $\mathrm{\Delta }{b}_2^{\text{T}}$ in two dimensions with two-body forces.

中文翻译：

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三体力在任意空间维度上被俘获和未被俘获的三分量费米子的病毒系数

使用粗糙的时间格近似，我们计算了具有三体接触相互作用的三物种费米子系统的病毒扩展的前几个项。 $d$ 在均质空间和频率的谐波捕获势中的空间尺寸 $\omega$。使用三体问题对正态化，我们报告了四阶和五阶维里系数的分析结果$\mathrm{\Delta }{b}_4$ 和 $\mathrm{\Delta }{b}_5$ 作为...的功能 $\mathrm{\Delta }{b}_3$。此外，我们认为$\omega \to 0$ 限制关系 $b_{ñ}^{\text{Ť}}={ñ}^{-d/2}{b}_{ñ}$对于任意温度和耦合强度（不仅限于标度不变的情况），在被捕获的温度（T）和均质系数之间保持一致。最后，我们指出了精确的，通用的（与频率和频率无关的）关系$\mathrm{\Delta }{b}_3^{\text{Ť}}$ 一维结合三体力 $\mathrm{\Delta }{b}_2^{\text{Ť}}$ 在二维中具有两体力。