二维费米子气体的Airy平均梯度修正
Airy-averaged gradient corrections for two-dimensional fermion gases
摘要：
基于PRA 93，042510（2016）中的讨论，我们提出了对动能泛函和单粒子密度的梯度校正的系统推导，特别是对于二维系统。我们从基于Wigner相空间形式主义的半经典展开中推导出领先的梯度修正，并证明了在零温度下的半经典动能密度泛函不能被明确地评估。相反，密度势函数描述，有效地结合相互作用提供了明确的梯度校正。采用平均过程，涉及艾里函数，从而部分地表示高阶梯度校正，我们促进了粒子密度的平滑过渡到经典的禁止区域的任意光滑的潜力。我们发现很好的协议的半经典Airy平均粒子密度与精确的密度非常低，但有限的温度，说明了一个费米气体与谐波势能。此外，我们提供的半经典展开在低温下的适用性的标准。最后，我们得到了一个表现良好的基态动能泛函，它改进了的K-Fermi近似。
英文摘要：
Building on the discussion in PRA 93, 042510 (2016), we present a systematic derivation of gradient corrections to the kinetic-energy functional and the one-particle density, in particular for two-dimensional systems. We derive the leading gradient corrections from a semiclassical expansion based on Wigner's phase space formalism and demonstrate that the semiclassical kinetic-energy density functional at zero temperature cannot be evaluated unambiguously. In contrast, a density-potential functional description that effectively incorporates interactions provides unambiguous gradient corrections. Employing an averaging procedure that involves Airy functions, thereby partially resumming higher-order gradient corrections, we facilitate a smooth transition of the particle density into the classically forbidden region of arbitrary smooth potentials. We find excellent agreement of the semiclassical Airy-averaged particle densities with the exact densities for very low but finite temperatures, illustrated for a Fermi gas with harmonic potential energy. We furthermore provide criteria for the applicability of the semiclassical expansions at low temperatures. Finally, we derive a well-behaved ground-state kinetic-energy functional, which improves on the Thomas-Fermi approximation.
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