Viscosity spectral functions of resonating fermions in the quantum virial expansion

Abstract

We consider two-component fermions with a zero-range interaction both in two and three dimensions and study their spectral functions of bulk and shear viscosities for an arbitrary scattering length. Here the Kubo formulas are systematically evaluated up to the second order in the quantum virial expansion applicable to the high-temperature regime. In particular, our computation of the bulk viscosity spectral function is facilitated by expressing it with the contact-contact response function, which can be measured experimentally under the periodic modulation of the scattering length. The obtained formulas are fully consistent with the known constraints on high-frequency tail and sum rule. Although our static shear viscosity agrees with that derived from the kinetic theory, our static bulk viscosity disagrees. Furthermore, the latter for three dimensions exhibits an unexpected non-analyticity of $\zeta \sim (\ln a^2)/a^2$ in the unitarity limit $a\to \infty$, which thus challenges the "crossover" hypothesis.

17 single-column pages, 1 multi-panel figure; (v2) minor improvements and added appendix A on the bulk viscosity formula at O(z^3); (v3) published version; (v4) corrected typos in Eq.(73) and added appendix B on the derivation of Eq.(67)

References in corpus (10)

• Viscosity in Strongly Interacting Quantum Field Theories from Black Hole Physics
• Viscosity Bound and Causality Violation
• Generalized Virial Theorem and Pressure Relation for a strongly correlated Fermi gas
• Effect of curvature squared corrections in AdS on the viscosity of the dual gauge theory
• Universal Quantum Viscosity in a Unitary Fermi Gas
• Exact Relations for a Strongly-interacting Fermi Gas from the Operator Product Expansion
• Beyond eta/s = 1/4pi
• Viscosity and scale invariance in the unitary Fermi gas
• Apparent low-energy scale invariance in two-dimensional Fermi gases
• Hydrodynamic tails and a fluctuation bound on the bulk viscosity

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