Density profile of noninteracting fermions in a rotating two-dimensional trap at finite temperature

We study the average density of $N$ spinless noninteracting fermions in a $2d$ harmonic trap rotating with constant frequency $\Omega$ and presence an additional repulsive central potential $\gamma/r^2$. The at zero temperature was recently studied Phys. Rev. A $\textbf{103}$, 033321 (2021) interesting multi-layered "wedding cake" structure "hole" center found for large limit. In this paper, we finite temperature. demonstrate how "wedding-cake" is modified These results warrant going much beyond standard Local Density Approximation. also generalize our to wide variety trapping potentials universality associated scaling functions both bulk edges "wedding-cake".