Work

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

Year: 2023

Type: article

Abstract: We study the average density of $N$ spinless noninteracting fermions in a two-dimensional harmonic trap rotating with a constant frequency $\mathrm{\ensuremath{\Omega}}$ and in the presence of an additional repulsive central potential $\ensuremath{\gamma}/{r}^{2}$. The average density at zero temperature was recently studied in Phys. Rev. A 103, 033321 (2021), and an interesting multilayered ``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. We show that, while the bulk density profile gets smeared significantly at a temperature $T\ensuremath{\sim}O(1)$, the edge profile already acquires significant smearing at a much lower temperature $T\ensuremath{\sim}O(1/\sqrt{N})$. 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 we demonstrate the universality of the associated scaling functions both in the bulk and at the edges of the ``wedding cake.''

Source: Physical Review A

DOI: 10.1103/physreva.107.023302

Authors: Manas Kulkarni, Pierre Le Doussal, Satya N. Majumdar, Grégory Schehr