We study the average density of N spinless noninteracting fermions in a 2d harmonic trap rotating with a constant frequency Ω and in the presence of an additional repulsive central potential γ/r2. The average density at zero temperature was recently studied in Phys. Rev. A 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".
@article{arxiv.2208.02458,
title = {Density profile of noninteracting fermions in a rotating $2d$ trap at finite temperature},
author = {Manas Kulkarni and Pierre Le Doussal and Satya N. Majumdar and Gregory Schehr},
journal= {arXiv preprint arXiv:2208.02458},
year = {2023}
}