Semi-classical limit of large fermionic systems at positive temperature

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 $\hslash =N^{-1/d}$ where $d$ is the space dimension, we prove the convergence to the corresponding Thomas-Fermi model at positive temperature.

arXiv commentConvergence of states rewritten. Some references added

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Cited by in corpus (3)

• Semiclassical approximation and critical temperature shift for weakly interacting trapped bosons
• Semiclassical limit for almost fermionic anyons
• Semi-classical limit of confined fermionic systems in homogeneous magnetic fields