Phonon contribution to the shear viscosity of a superfluid Fermi gas in the unitarity limit

Abstract

We present a detailed analysis of the contribution of small-angle Nambu-Goldstone boson (phonon) collisions to the shear viscosity, η, in a superfluid atomic Fermi gas close to the unitarity limit. We show that the experimental values of the shear viscosity coefficient to entropy ratio, η/s, obtained at the lowest reached temperature can be reproduced assuming that phonons give the leading contribution to η. The phonon contribution is evaluated considering 1 ↔ 2 processes and taking into account the finite size of the experimental system. In particular, for very low temperatures, T < ∼ 0.1TF , we find that phonons are ballistic and the contribution of phonons to the shear viscosity is determined by the processes that take place at the interface between the superfluid and the normal phase. This result is independent of the detailed form of the phonon dispersion law and leads to two testable predictions: the shear viscosity should correlate with the size of the optical trap and it should decrease with decreasing temperature. For higher temperatures the detailed form of the phonon dispersion law becomes relevant and, within our model, we find that the experimental data for η/s can be reproduced assuming that phonons have an anomalous dispersion law.

Transport coefficients in superfluid neutron stars

“…2 we show that the shear viscosity due to the binary collisions of superfluid phonons scales with temperature as 1/T 5 . This indeed results from a very simple dimensional analysis and it is a universal feature that occurs in other superfluid systems such as 4 He [12] or superfluid cold atoms at unitary [19,20]. The choice of EoS determines the exact numerical values of η.…”

Trapped phonons

“…This expression has been used in the study of the oscillations of compact stars in [6,7], for the description of the oscillations of objects immersed in 4 He, see e.g. [8], and for the breathing mode of ultracold fermionic atoms (discussed below) in [1,2].…”

“…whereγ 0.18 (see [12,13,14] and the discussion in [2]), and a numerical estimate ofδ was obtained in [1,2] from a fit of the experimental values of the shear viscosity to entropy ratio. Indeed the contribution of binary (hereafter 4ph) and 1 ↔ 2 (hereafter 3ph) processes to the shear viscosity depends on the phonon dispersion law and in Refs.…”

“…For an optically trapped superfluid our results corroborate the findings of Refs. [1,2], which imply that at very low temperature the shear viscosity correlates with the size of the optical trap and decreases with decreasing temperature.Xth Quark Confinement and the Hadron Spectrum, …”

Shear and bulk viscosities of a photon gas at low temperature

“…Under current discussion is the behavior of the bulk viscosity [4] and whether [5,6] or not [7] there is a maximum of the bulk viscosity in the same crossover region. Also well known are the transport coefficients in perturbative quantum chromodynamics (QCD) [8], as well as the lowenergy pion gas [9,10] and strongly coupled Fermi systems [11].…”