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Register a new userMultilayered density profile for noninteracting fermions in a rotating two-dimensional trap
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We compute exactly the average spatial density for $N$ spinless noninteracting fermions in a $2d$ harmonic trap rotating with a constant frequency $Omega$ in the presence of an additional repulsive central potential $gamma/r^2$. 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 $Omega$ and $gamma$ 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.
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