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26 April 2024
 
  » arxiv » 1008.0007

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Viscosity and scale invariance in the unitary Fermi gas
Tilman Enss ; Rudolf Haussmann ; Wilhelm Zwerger ;
Date 30 Jul 2010
AbstractWe 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 $eta(omega)$ exhibits a Drude-like transport peak and a power-law tail at large frequencies that is proportional to the Tan contact. The weight in the transport peak is given by the equilibrium energy density, consistent with a sum rule that has recently been derived by Taylor and Randeria. Near the superfluid transition, the peak width is of the order $0.5, T_F$, thus invalidating a quasiparticle description. The ratio $eta/s$ 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 $hbar/(4pi k_B)$ by a factor of about seven.
Source arXiv, 1008.0007
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