# 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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Journal articles
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https://hal.archives-ouvertes.fr/hal-03179775
Contributor : Claudine Le Vaou <>
Submitted on : Wednesday, March 24, 2021 - 2:36:35 PM
Last modification on : Friday, March 26, 2021 - 3:31:24 AM

### Citation

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

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