Viscosity Sum Rules at Large Scattering Lengths

Abstract

We use the operator product expansion (OPE) and dispersion relations to obtain new model-independent "Borel-resummed" sum rules for both shear and bulk viscosity of many-body systems of spin-1/2 fermions with predominantly short range S-wave interactions. These sum rules relate Gaussian weights of the frequency-dependent viscosities to the Tan contact parameter C(a). Our results are valid for arbitrary values of the scattering length a, but receive small corrections from operators of dimension larger than 5 in the OPE, and can be used to study transport properties in the vicinity of the infinite scattering length fixed point. In particular, we find that the exact dependence of the shear viscosity sum rule on scattering length is controlled by the function C(a). The sum rules that we obtain depend on a frequency scale w that can be optimized to maximize their overlap with low-energy data.

References in corpus (17)

• Generalized Virial Theorem and Pressure Relation for a strongly correlated Fermi gas
• Nonrelativistic conformal field theories
• Exact Relations for a Strongly-interacting Fermi Gas from the Operator Product Expansion
• Number of closed-channel molecules in the BEC-BCS crossover
• Universal Properties of the Ultra-Cold Fermi Gas
• Viscosity and scale invariance in the unitary Fermi gas
• Tan relations in one dimension
• Universal Relations for Identical Bosons from 3-Body Physics
• Theory of RF-spectroscopy of strongly interacting Fermions
• Viscosity of strongly interacting quantum fluids: spectral functions and sum rules
• Short-Time Operator Product Expansion for rf Spectroscopy of a Strongly-interacting Fermi Gas
• Coherence and clock shifts in ultracold Fermi gases with resonant interactions
• Universal Short-Distance Structure of the Single-Particle Spectral Function of Dilute Fermi Gases
• Short-distance and short-time structure of a unitary Fermi gas
• Current response, structure factor and hydrodynamic quantities of a two- and three-dimensional Fermi gas from the operator-product expansion
• Static structure factor of a strongly correlated Fermi gas at large momenta
• Viscosity spectral functions of the dilute Fermi gas in kinetic theory

Cited by in corpus (20)

• Quantum mechanical limitations to spin diffusion in the unitary Fermi gas
• Shear Viscosity of a Unitary Fermi Gas
• Bulk viscosity and contact correlations in attractive Fermi gases
• Vortices and vortex lattices in quantum ferrofluids
• High-temperature expansion of the viscosity in interacting quantum gases
• Hydrodynamic tails and a fluctuation bound on the bulk viscosity
• Shear viscosity and damping of collective modes in a two-dimensional Fermi gas
• OPE convergence in non-relativistic conformal field theories
• Probing strongly interacting atomic gases with energetic atoms
• Constraining quantum critical dynamics: 2+1D Ising model and beyond
• Effective theory and universal relations for Fermi gases near a $d$-wave interaction resonance
• The Operator Product Expansion Beyond Leading Order for Two-Component Fermions
• Shear viscosity and Strong-Coupling Corrections in the BCS-BEC crossover Regime of an Ultracold Fermi Gas
• Shear viscosity and spin sum rules in strongly interacting Fermi gases
• Single-particle spectral density of the unitary Fermi gas: Novel approach based on the operator product expansion, sum rules and the maximum entropy method
• Hydrodynamic Attractor in Ultracold Atoms
• Bulk viscosity and conformal symmetry breaking in the dilute Fermi gas near unitarity
• Viscosity spectral function of a scale invariant non-relativistic fluid from holography
• Bulk viscosity of dual Bose and Fermi gases in one dimension
• Kovtun-Son-Starinets Conjecture and Effects of Mass Imbalance in the Normal State of an Ultracold Fermi Gas in the BCS-BEC Crossover Region