Correlation Energy of a Weakly Interacting Fermi Gas with Large Interaction Potential
Niels Benedikter, Marcello Porta, Benjamin Schlein, Robert Seiringer
Abstract
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 $$|\cdot | \hat{V} \in \ell ^1 (\mathbb {Z}^3)$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:mrow><mml:mrow><mml:mo>|</mml:mo><mml:mo>·</mml:mo><mml:mo>|</mml:mo></mml:mrow><mml:mover><mml:mi>V</mml:mi><mml:mo>^</mml:mo></mml:mover><mml:mo>∈</mml:mo><mml:msup><mml:mi>ℓ</mml:mi><mml:mn>1</mml:mn></mml:msup><mml:mrow><mml:mo>(</mml:mo><mml:msup><mml:mrow><mml:mi>Z</mml:mi></mml:mrow><mml:mn>3</mml:mn></mml:msup><mml:mo>)</mml:mo></mml:mrow></mml:mrow></mml:math> . 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.