Viscosity and scale invariance in the unitary Fermi gas
arXiv:1008.0007 · doi:10.1016/j.aop.2010.10.002
Abstract
We compute the shear viscosity of the unitary Fermi gas above the superfluid transition temperature, using a diagrammatic technique that starts from the exact Kubo formula. The formalism obeys a Ward identity associated with scale invariance which guarantees that the bulk viscosity vanishes identically. For the shear viscosity, vertex corrections and the associated Aslamazov-Larkin contributions are shown to be crucial to reproduce the full Boltzmann equation result in the high-temperature, low fugacity limit. The frequency dependent shear viscosity exhibits a Drude-like transport peak and a power-law tail at large frequencies which is proportional to the Tan contact. The weight in the transport peak is given by the equilibrium pressure, in agreement with a sum rule due to Taylor and Randeria. Near the superfluid transition the peak width is of the order of , thus invalidating a quasiparticle description. The ratio between the static shear viscosity and the entropy density exhibits a minimum near the superfluid transition temperature whose value is larger than the string theory bound by a factor of about seven.
34 pages, 9 figures; final form (contains new derivation of sum rule), accepted for publication in Annals of Physics
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