The Random Phase Approximation for Interacting Fermi Gases in the Mean-Field Regime
Abstract
We present a general approach to justify the random phase approximation for the homogeneous Fermi gas in three dimensions in the mean-field scaling regime. We consider a system of $N$ fermions on a torus, interacting via a two-body repulsive potential proportional to $N^{-\frac{1}{3}}$. In the limit $N\to\infty$, we derive the exact leading order of the correlation energy and the bosonic elementary excitations of the system, which are consistent with the prediction of the random phase approximation in the physics literature.
- Publication:
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arXiv e-prints
- Pub Date:
- June 2021
- DOI:
- 10.48550/arXiv.2106.11161
- arXiv:
- arXiv:2106.11161
- Bibcode:
- 2021arXiv210611161R
- Keywords:
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- Mathematical Physics;
- Condensed Matter - Quantum Gases;
- Condensed Matter - Strongly Correlated Electrons
- E-Print:
- Final version to appear in Forum Math. Pi (124 pages), plus a supplementary note (15 pages)