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arXiv · 2208.02458

Density profile of noninteracting fermions in a rotating $2d$ trap at finite temperature

Manas Kulkarni·Pierre Le Doussal·Satya N. Majumdar·Gregory Schehr
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Abstract

We study the average density of $N$ spinless noninteracting fermions in a $2d$ harmonic trap rotating with a constant frequency $\Omega$ and in the presence of an additional repulsive central potential $\gamma/r^2$. 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".

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Manas Kulkarni, Pierre Le Doussal, Satya N. Majumdar, Gregory Schehr. 2022-08-04. Density profile of noninteracting fermions in a rotating $2d$ trap at finite temperature. https://doi.org/10.1103/physreva.107.023302

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