论文标题
在有限温度下旋转$ 2D $陷阱中非互动费米子的密度曲线
Density profile of noninteracting fermions in a rotating $2d$ trap at finite temperature
论文作者
论文摘要
我们研究了$ N $无自旋非互动费米的平均密度，在$ 2D $谐波陷阱中以恒定的频率$ω$旋转，并且在存在附加的排斥性中心电位$γ/r^2 $的情况下。最近在物理中研究了零温度下的平均密度。 Rev. a $ \ textbf {103} $，033321（2021）和一个有趣的多层“婚礼蛋糕”结构，在中心发现了一个“孔”，在大$ n $ limit中的密度都在中心。在本文中，我们研究有限温度下的平均密度。我们演示了如何在有限温度下修改这种“婚礼蛋糕”结构。这些大的$ n $结果保证令超出了标准的局部密度近似值。我们还将结果推广到各种各样的诱捕电位，并在“婚礼蛋糕”的批量和边缘都展示了相关缩放函数的普遍性。
We study the average density of $N$ spinless noninteracting fermions in a $2d$ harmonic trap rotating with a constant frequency $Ω$ and in the presence of an additional repulsive central potential $γ/r^2$. The average density at zero temperature was recently studied in Phys. Rev. A $\textbf{103}$, 033321 (2021) and an interesting multi-layered "wedding cake" structure with a "hole" at the center was found for the density in the large $N$ limit. In this paper, we study the average density at finite temperature. We demonstrate how this "wedding-cake" structure is modified at finite temperature. These large $N$ results warrant going much beyond the standard Local Density Approximation. We also generalize our results to a wide variety of trapping potentials and demonstrate the universality of the associated scaling functions both in the bulk and at the edges of the "wedding-cake".
