Shear viscosity and spin sum rules in strongly interacting Fermi gases

TL;DR

This paper investigates the universal high-frequency tails of spin conductivity and shear viscosity spectral functions in strongly interacting Fermi gases, deriving related sum rules and analyzing their implications in different dimensions.

Contribution

It derives the spin f-sum rule unaffected by high-frequency tails and shows how viscosity tails modify the shear viscosity sum rule in Fermi gases.

Findings

Spin conductivity spectral function exhibits universal power-law tails.

The spin f-sum rule remains unaffected by high-frequency tails in dimensions less than four.

Viscosity spectral function tails modify the shear viscosity sum rule.

Abstract

Fermi gases with short-range interactions are ubiquitous in ultracold atomic systems. In the absence of spin-flipping processes the number of atoms in each spin species is conserved separately, and we discuss the associated Ward identities. For contact interactions the spin conductivity spectral function sigma_s(omega) has universal power-law tails at high frequency. We derive the spin f-sum rule and show that it is not affected by these tails in d<4 dimensions. Likewise the shear viscosity spectral function eta(omega) has universal tails; in contrast they modify the viscosity sum rule in a characteristic way.