The Random Phase Approximation for Interacting Fermi Gases in the MeanField Regime
Abstract
We present a general approach to justify the random phase approximation for the homogeneous Fermi gas in threedimensions in the meanfield scaling regime. We consider a system of $N$ fermions on a torus, interacting via a twobody repulsive potential proportional to $N^{\frac{1}{3}}$. In the limit $N\rightarrow\infty$, we derive the exact leading order of the correlation energy and the elementary excitations of the system, which are consistent with the prediction of GellMann and Brueckner in 1957.
 Publication:

arXiv eprints
 Pub Date:
 June 2021
 arXiv:
 arXiv:2106.11161
 Bibcode:
 2021arXiv210611161R
 Keywords:

 Mathematical Physics;
 Condensed Matter  Quantum Gases;
 Condensed Matter  Strongly Correlated Electrons
 EPrint:
 New version with new results on elementary excitations, 127 pages