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Multilayered density profile for noninteracting fermions in a rotating two-dimensional trap

Abstract

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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Dates and versions

hal-03179775 , version 1 (16-12-2023)

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Manas Kulkarni, Satya N. Majumdar, Grégory Schehr. Multilayered density profile for noninteracting fermions in a rotating two-dimensional trap. Physical Review A, 2021, 103 (3), ⟨10.1103/PhysRevA.103.033321⟩. ⟨hal-03179775⟩
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