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

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 η/s > 4.7 times the proposed lower bound of /4πk B which came from the AdS/CFT correspondence 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 η/s > 1.3 times the bound.

Quantum Bose and Fermi gases with large negative scattering length in the two-bodyS-matrix approximation

“…(8), q,c → 2q,2c, with Eqs. (17) and (18) still valid. In other words, henceforth, q,c will refer to one of the two components.…”

“…For instance, it was applied to the so-called unitary limit in three dimensions where the scattering length diverges and the S matrix becomes simply −1, and reasonable results were obtained for the critical temperature [15,16]. The ratio of the viscosity to entropy density was also calculated using this method [17] and agrees well with the most recent experiments [18]. Thus, although the method cannot really compete with numerical methods such as Monte Carlo, it can be justified as an exploratory tool for regimes that have not been extensively studied.…”

First and second sound in a highly elongated Fermi gas at unitarity

“…This correction is imaginary and corresponds to damping. Near T c , employing the notion of "minimal quantum viscosity" [58], one finds δc/c = −iAmn 1 ω/η, where η is the viscosity calculated on the symmetry axis and A ∼ 8.12 × 10 −4 . In the high T classical limit one instead finds A ∼ 1.62 × 10 −3 .…”

On the ratio of the shear viscosity to the density of entropy of the rare gases and H2,N2,

“…Müller et al [9] studied the ratio g=s of graphene and also found j > j 0 in that case. Two-dimensional Fermi gases also obey the inequality j > j 0 [10,11]. Csernai et al [12] pointed out some similarities between the general behavior of j near the critical points of He, N 2 , and H 2 O and that of the phase transition from hadrons to the quark-gluon plasma.…”