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On the correlation energy of the mean-field Fermi gas

Christian Hainzl, Marcello Porta, Felix Rexze

Published Jun 29, 2018• 3 citations
OpenAlex

Abstract

We consider a system of $N\gg 1$ interacting fermionic particles in three dimensions, confined in a periodic box of volume $1$, in the mean-field scaling. We assume that the interaction potential is bounded and small enough. We prove upper and lower bounds for the correlation energy, which are optimal in their $N$-dependence. Moreover, we compute the correlation energy at leading order in the interaction potential, recovering the prediction of second order perturbation theory. The proof is based on the combination of recent methods introduced in the context of fermionic many-body quantum dynamics together with a rigorous version of second-order perturbation theory, developed in the context of non-relativistic QED.

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