Short-distance and short-time structure of a unitary Fermi gas

TL;DR

This paper analyzes the short-distance and short-time behavior of a unitary Fermi gas using operator product expansions, deriving analytic expressions for the dynamic structure factor and energy response related to Tan's contact parameter.

Contribution

It provides the first analytic calculation of the dynamic structure factor S(q,w) at large frequencies and momenta for a unitary Fermi gas, linking it to Tan's contact.

Findings

Derived closed-form expressions for S(q,w) at high frequencies and momenta.

Linked the normalization of S(q,w) to Tan's contact parameter.

Quantified energy deposition from rapid changes in scattering length.

Abstract

We consider the operator product expansions for unitarity fermions. We compute the dynamic structure factor S(q,w) at large frequency and wavenumber away from the one-particle peak. The overall normalization of S(q,w) is determined by Tan's contact parameter, and the dependence on q and w is obtained in closed analytic form. We also find energy deposited into the system by small, rapid variations of the inverse scattering length.