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

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 $\text{103}$, 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".

18 pages, 7 figures, 1 table

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• Spatio-temporal fluctuations in the passive and active Riesz gas on the circle
• Linear statistics at the microscopic scale for the 2D Coulomb gas
• Exact first-order effect of interactions on the ground-state energy of harmonically-confined fermions