Correlation Energy of a Weakly Interacting Fermi Gas with Large Interaction Potential

Abstract

Recently the leading order of the correlation energy of a Fermi gas in a coupled mean-field and semiclassical scaling regime has been derived, under the assumption of an interaction potential with a small norm and with compact support in Fourier space. We generalize this result to large interaction potentials, requiring only $|\cdot |\hat{V}\in {\ell }^1({\mathbb{Z}}^3)$. Our proof is based on approximate, collective bosonization in three dimensions. Significant improvements compared to recent work include stronger bounds on non-bosonizable terms and more efficient control on the bosonization of the kinetic energy.

arXiv comment50 pages; v4: Lemma 7.2 simplified (log-corrections removed)

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• Bosonization of Fermionic Many-Body Dynamics
• The Huang-Yang formula for the low-density Fermi gas: upper bound
• Bosonized Momentum Distribution of a Fermi Gas via Friedrichs Diagrams
• Exact first-order effect of interactions on the ground-state energy of harmonically-confined fermions
• Dynamics of mean-field Fermi systems with nonzero pairing
• Effective Polaron Dynamics of an Impurity Particle Interacting with a Fermi Gas