# Semi-classical limit of large fermionic systems at positive temperature

## TL;DR

This paper investigates the behavior of large interacting fermionic systems at positive temperature, demonstrating their convergence to the Thomas-Fermi model in a semi-classical limit with specific scaling parameters.

## Contribution

It establishes the convergence of large fermionic systems to the Thomas-Fermi model at positive temperature under a particular semi-classical scaling regime.

## Key findings

- Convergence to Thomas-Fermi model proven at positive temperature
- Semi-classical limit characterized by specific scaling of interaction and Planck's constant
- Results applicable to systems in any spatial dimension d

## Abstract

We study a system of $N$ interacting fermions at positive temperature in a confining potential. In the regime where the intensity of the interaction scales as $1/N$ and with an effective semi-classical parameter $\hbar=N^{-1/d}$ where $d$ is the space dimension, we prove the convergence to the corresponding Thomas-Fermi model at positive temperature.