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.

arXiv comment17 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 (28)

• Feshbach Resonances in Ultracold Gases
• Viscosity in Strongly Interacting Quantum Field Theories from Black Hole Physics
• Universality in Few-body Systems with Large Scattering Length
• Large momentum part of fermions with large scattering length
• Energetics of a strongly correlated Fermi gas
• Viscosity Bound Violation in Higher Derivative Gravity
• Viscosity Bound and Causality Violation
• Nearly Perfect Fluidity: From Cold Atomic Gases to Hot Quark Gluon Plasmas
• 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
• Strongly Correlated Quantum Fluids: Ultracold Quantum Gases, Quantum Chromodynamic Plasmas, and Holographic Duality
• Viscosity and scale invariance in the unitary Fermi gas
• Tan relations in one dimension
• Viscosity of strongly interacting quantum fluids: spectral functions and sum rules
• Virial expansion for a strongly correlated Fermi system and its application to ultracold atomic Fermi gases
• Viscosity and Thermal Relaxation for a resonantly interacting Fermi gas
• Apparent low-energy scale invariance in two-dimensional Fermi gases
• Observation of conformal symmetry breaking and scale invariance in expanding Fermi gases
• Anomalous minimum in the shear viscosity of a Fermi gas
• Current response, structure factor and hydrodynamic quantities of a two- and three-dimensional Fermi gas from the operator-product expansion
• Scale breaking and fluid dynamics in a dilute two-dimensional Fermi gas
• Hydrodynamic tails and a fluctuation bound on the bulk viscosity
• Shear viscosity and spin diffusion coefficient of a two-dimensional Fermi gas
• Efimov correlations in strongly interacting Bose gases
• Hydrodynamics with spacetime-dependent scattering length

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• The Role of the Effective Range in Resonantly Interacting Fermi Gases: How Breaking Scale Symmetry Affects the Bulk Viscosity
• Bulk viscosity of resonating fermions revisited: Kubo formula, sum rule, and the dimer and high-temperature limits
• Virial Expansion for a Three-Component Fermi Gas in One Dimension: The Quantum Anomaly Correspondence
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• Bulk viscosity of dual Bose and Fermi gases in one dimension
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• Thermodynamic contacts and breathing mode physics of 1D p-wave Fermi gases in the high temperature limit
• Viscous Flow in a 1D Spin-Polarized Fermi Gas: the Role of Integrability on Viscosity
• Emergent Infrared Conformal Dynamics in Strongly Interacting Quantum Gases
• Particle and pair spectra for strongly correlated Fermi gases: A real-frequency solver
• Scale and conformal invariance in rotating interacting few-fermion systems
• Dispersion of first sound in a weakly interacting ultracold Fermi liquid
• Hydrodynamic attractor in periodically driven ultracold quantum gases
• Exact perturbative expansion of the transport coefficients of a normal low-temperature Fermi gas with contact interactions
• Dimer-projection contact and the clock shift of a unitary Fermi gas
• Viscous Drude weight of dual Bose and Fermi gases in one dimension
• Quench Dynamics of Thermal Bose Gases Across Wide and Narrow Feshbach
• Quantum transport in strongly correlated Fermi gases
• Toward an automated-algebra framework for high orders in the virial expansion of quantum matter
• Pair-Condensation Peak in Radio-Frequency Dimer-Projection Spectroscopy of a Unitary Fermi Gas