On the viscosity to entropy density ratio for unitary Bose and Fermi Gases

TL;DR

This paper calculates the viscosity to entropy density ratio for unitary Bose and Fermi gases using a new S-matrix based approach, revealing their fluidity and phase transition behaviors.

Contribution

It introduces a novel method to compute eta/s for gases at unitarity, providing insights into their fluid properties and phase transitions.

Findings

Fermionic gases have eta/s > 4.7 times the AdS/CFT bound, consistent with experiments.

Bosonic gases likely undergo a phase transition to a Bose-Einstein condensate.

Bosonic gases are more perfect fluids with eta/s > 1.3 times the bound.

Abstract

We calculate the ratio of the viscosity to the entropy density for both Bose and Fermi gases in the unitary limit using a new approach to the quantum statistical mechanics of gases based on the S-matrix. In the unitary limit the scattering length diverges and the S-matrix equals -1. For the fermion case we obtain eta/s > 4.7 times the proposed lower bound of \hbar/4 pi k_B which came from the AdS/CFT for gauge theories, consistent with the most recent experiments. For the bosonic case we present evidence that the gas undergoes a phase transition to a strongly interacting Bose-Einstein condensate, and is a more perfect fluid, with eta/s > 1.3 times the bound.