We study a system of trapped two-component Fermi gases with a zero-range interaction in two dimensions or one dimension. We calculate the one-particle density matrices of these systems at small displacements, from which we show that the $N$-body energies are linear functionals of the occupation probabilities of single-particle energy eigenstates. A universal energy functional was first derived in 2011 [S. Tan, Phys. Rev. Lett. 107, 145302 (2011)] for trapped zero-range interacting two-component Fermi gases in three dimensions. We also calculate the asymptotic behaviors of the occupation probabilities of single-particle energy eigenstates at high energies.

中文翻译：

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低维中俘获费米气体的通用能量泛函

我们研究了一种在二维或一维中具有零程相互作用的被捕获的双组分费米气体系统。我们计算了这些系统在小位移下的单粒子密度矩阵，从中我们表明$氮$-体能量是单粒子能量本征态占据概率的线性函数。通用能量泛函于 2011 年首次导出 [S.谭，物理。莱特牧师。 107 , 145302 (2011)]用于三维空间中捕获的零范围相互作用的双组分费米气体。我们还计算了高能下单粒子能量本征态的占据概率的渐近行为。