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 semiclassical parameter ℏ = N−1/d where d is the space dimension, we prove the convergence to the corresponding Thomas-Fermi model at positive temperature.
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53 works under the condition that for some a > 0 for large p. Not all interaction potentials can, therefore, be covered.
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