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

TL;DR

This paper investigates how the density profile of noninteracting fermions in a rotating 2D trap changes at finite temperature, revealing modifications to the multi-layered structure and demonstrating universality across various potentials.

Contribution

It extends previous zero-temperature studies to finite temperature, analyzing the density profile and showing the universality of scaling functions beyond local density approximation.

Findings

Finite temperature modifies the 'wedding-cake' density structure.

Universality of scaling functions at bulk and edges.

Generalization to various trapping potentials.

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".