论文标题
旋转二维陷阱中非互动费米的多层密度曲线
Multilayered density profile for noninteracting fermions in a rotating two-dimensional trap
论文作者
论文摘要
我们准确地计算出$ N $无旋转非互动费米的平均空间密度在$ 2D $谐波陷阱中以恒定频率$ω$旋转，并在额外的排斥中心电位$γ/r^2 $的情况下。我们发现，在$ n $限制的情况下，散装密度具有丰富而非平凡的轮廓 - 陷阱的中心有一个洞，并被多层的“婚礼蛋糕”结构所包围。层的数量取决于$ n $以及两个参数$ω$和$γ$，从而导致了丰富的相图。放大$ k^{\ rm th} $ layer的边缘，我们发现边缘密度配置文件显示$ k $ kinks位于$ k^{\ rm th} $ hermite polynomial的零。有趣的是，在大$ k $限制中，我们表明边缘密度曲线接近限制形式，类似于传播前部的形状，在某些量子旋转链的单一演变中发现。我们还研究新形成的液滴如何在最后一层的顶部大小生长，因为一个液滴会更改参数。
We compute exactly the average spatial density for $N$ spinless noninteracting fermions in a $2d$ harmonic trap rotating with a constant frequency $Ω$ in the presence of an additional repulsive central potential $γ/r^2$. We find that, in the large $N$ limit, the bulk density has a rich and nontrivial profile -- with a hole at the center of the trap and surrounded by a multi-layered "wedding cake" structure. The number of layers depends on $N$ and on the two parameters $Ω$ and $γ$ leading to a rich phase diagram. Zooming in on the edge of the $k^{\rm th}$ layer, we find that the edge density profile exhibits $k$ kinks located at the zeroes of the $k^{\rm th}$ Hermite polynomial. Interestingly, in the large $k$ limit, we show that the edge density profile approaches a limiting form, which resembles the shape of a propagating front, found in the unitary evolution of certain quantum spin chains. We also study how a newly formed droplet grows in size on top of the last layer as one changes the parameters.
