Semi-classical limit of large fermionic systems at positive temperature

Mathieu Lewin (1, 2, 3) , Peter S Madsen (4) , Arnaud Triay (1, 3)

1 CEREMADE - CEntre de REcherches en MAthématiques de la DEcision
2 CNRS - Centre National de la Recherche Scientifique
3 PSL - Université Paris Sciences et Lettres
4 Aarhus University [Aarhus]

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 .

Domaines: Physique mathématique [math-ph]; Equations aux dérivées partielles [math.AP]

Mathieu Lewin, Peter S Madsen, Arnaud Triay. Semi-classical limit of large fermionic systems at positive temperature. Journal of Mathematical Physics, 2019, 60, pp.091901. ⟨10.1063/1.5094397⟩. ⟨hal-02007704⟩