Semi-classical limit of large fermionic systems at positive temperature

Arnaud Triay; Mathieu Lewin; Peter S. Madsen

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Semi-classical limit of large fermionic systems at positive temperature

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arxiv 1902.00310 v2 pith:3O6JJHPB submitted 2019-02-01 math-ph math.APmath.MP

Semi-classical limit of large fermionic systems at positive temperature

Mathieu Lewin , Peter S. Madsen , Arnaud Triay This is my paper

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keywords positivetemperaturesemi-classicalconfiningconvergencecorrespondingdimensioneffective

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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.

Semi-classical limit of large fermionic systems at positive temperature

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