Current response, structure factor and hydrodynamic quantities of a two- and three-dimensional Fermi gas from the operator-product expansion

TL;DR

This paper uses the operator-product expansion to analyze the high-frequency response and hydrodynamic properties of 2D and 3D Fermi gases, providing exact contact coefficients and sum rules for viscosities.

Contribution

It introduces an application of the operator-product expansion to Fermi gases, deriving exact coefficients and sum rules for response functions and viscosities.

Findings

Exact contact coefficient determined for high-frequency response.

Derived sum rules for spectral viscosities.

Calculated dynamic structure factor and high-frequency tails.

Abstract

We apply the operator-product expansion to determine the asymptotic form of the current response of a Fermi gas in two and three dimensions. The leading-order term away from the one-particle peak is proportional to a quantity known as the contact, the coefficient of which is determined exactly. We also calculate the dynamic structure factor and the high-frequency tails of the spectral viscosities as a function of the scattering length. Our results are used to derive certain sum rules for the viscosities.