Viscosity of an ideal relativistic quantum fluid: A perturbative study

We show that a quantized ideal fluid will generally exhibit a small but nonzero viscosity due to the backreaction of quantum sound waves on the background. We use an effective field theory expansion to estimate this viscosity to leading order in perturbation theory. We discuss our results and whether this estimate can be used to obtain a more model-independent estimate of the “quantum bound” on the viscosity of physical systems.

Figure 1

Diagrammatic illustration for the equivalence between Kubo and Boltzmann relations for the transport coefficient at tree level. See 24 for a derivation.

Figure 2

$\eta /s$, in arbitrary units, as a function of $c_T$, $g$, $\Lambda$ for the two equations of state (the ideal EoS is shown by a solid black line, and the crossover EoS by a dashed red line). The other parameters are fixed at unity in arbitrary units. The plot is truncated when, at large values of $g$ and high values of $\Lambda$, the calculation of $\eta /s$ becomes numerically unstable because the integrand from 0 to $\Lambda$ is dominated by very small values.

Figure 3

“Renormalized” $\eta /s$ for the two equations of state (the ideal EoS is shown by a solid black line, and the crossover EoS by a dashed red line).