幺正费米气体的扩展的D-F密度泛函
Extended Thomas-Fermi Density Functional for the Unitary Fermi Gas
摘要：
基于最近的扩散蒙特卡罗（DMC）计算[Phys.Rev.Lett.]，我们确定了具有无限散射长度的被捕获的二组分费米气体（酉费米气体）的能量密度$ξ(3/5) n ε_F$和扩展的费米（ETF）密度泛函的梯度校正$λ\hbar^2(\nabla n)^2/(8m n)$，其中$n$是数密度，$ε_F$是费米能量。{ \bf 99}，233201（2007）]。特别地，我们发现，$ξ=0.455$和$λ=0.13$给出了具有偶数个$N$颗粒的DMC数据的最佳拟合。我们还研究了频率为$ω$的谐振势阱中幺正气体基态能量的奇偶分裂$γN^{1/9} \hbar ω$，确定了常数$γ$。最后通过引入广义Galilei不变流体动力学方程，研究了梯度项在含时ETF模型中的作用。
英文摘要：
We determine the energy density $ξ(3/5) n ε_F$ and the gradient correction $λ\hbar^2(\nabla n)^2/(8m n)$ of the extended Thomas-Fermi (ETF) density functional, where $n$ is number density and $ε_F$ is Fermi energy, for a trapped two-components Fermi gas with infinite scattering length (unitary Fermi gas) on the basis of recent diffusion Monte Carlo (DMC) calculations [Phys. Rev. Lett. {\bf 99}, 233201 (2007)]. In particular we find that $ξ=0.455$ and $λ=0.13$ give the best fit of the DMC data with an even number $N$ of particles. We also study the odd-even splitting $γN^{1/9} \hbar ω$ of the ground-state energy for the unitary gas in a harmonic trap of frequency $ω$ determining the constant $γ$. Finally we investigate the effect of the gradient term in the time-dependent ETF model by introducing generalized Galilei-invariant hydrodynamics equations.
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