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

Abstract

AbstractRecently 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$$|\cdot | \hat{V} \in \ell ^1 (\mathbb {Z}^3)$$|·|V^∈ℓ1(Z3). 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.