Current response, structure factor and hydrodynamic quantities of a two- and three-dimensional Fermi gas from the operator-product expansion

Abstract

We apply the operator-product expansion to determine the asymptotic form of the current response of a Fermi gas in two and three dimensions. The leading-order term away from the one-particle peak is proportional to a quantity known as the contact, the coefficient of which is determined exactly. We also calculate the dynamic structure factor and the high-frequency tails of the spectral viscosities as a function of the scattering length. Our results are used to derive certain sum rules for the viscosities.

14 pages, 10 figures

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• Quantum Monte Carlo approaches to nuclear and atomic physics
• Observation of quantum-limited spin transport in strongly interacting two-dimensional Fermi gases
• Contact and sum-rules in a near-uniform Fermi gas at unitarity
• Fluid Dynamics and Viscosity in Strongly Correlated Fluids
• Scale breaking and fluid dynamics in a dilute two-dimensional Fermi gas
• Clock shift in a strongly interacting two-dimensional Fermi gas
• Contact and Momentum Distribution of the Unitary Fermi Gas
• Bulk viscosity and contact correlations in attractive Fermi gases
• High-temperature expansion of the viscosity in interacting quantum gases
• Pairing effects in the non-degenerate limit of the two-dimensional Fermi gas
• Viscosity spectral functions of resonating fermions in the quantum virial expansion
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• Shear viscosity and damping of collective modes in a two-dimensional Fermi gas
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• Universal Spin Transport and Quantum Bounds for Unitary Fermions
• Field-theoretical aspects of one-dimensional Bose and Fermi gases with contact interactions
• OPE convergence in non-relativistic conformal field theories
• Probing strongly interacting atomic gases with energetic atoms
• Few-fermion systems in one dimension: Ground- and excited-state energies and contacts
• Universal Noise in Continuous Transport Measurements of Interacting Fermions
• Viscosity Sum Rules at Large Scattering Lengths
• Short-distance properties of Coulomb systems
• Effective theory and universal relations for Fermi gases near a $d$-wave interaction resonance
• Perfect-fluid behavior of a dilute Fermi gas near unitary
• Deep inelastic scattering on ultracold gases
• Universal relations for dipolar quantum gases
• Second order fluid dynamics for the unitary Fermi gas from kinetic theory
• Tan's contact and the phase distribution of repulsive Fermi gases: Insights from QCD noise analyses
• The Operator Product Expansion Beyond Leading Order for Two-Component Fermions
• Contact formalism for coupled channels
• Single-particle spectral density of the unitary Fermi gas: Novel approach based on the operator product expansion, sum rules and the maximum entropy method
• Shear viscosity and spin sum rules in strongly interacting Fermi gases
• Hydrodynamic Attractor in Ultracold Atoms
• Bulk viscosity and conformal symmetry breaking in the dilute Fermi gas near unitarity
• Universal relations for hybridized $s$- and $p$-wave interactions from spin-orbital coupling
• Universal relations and normal-state properties of a Fermi gas with laser-dressed mixed-partial-wave interactions
• Optical spin conductivity in ultracold quantum gases
• Viscosity spectral function of a scale invariant non-relativistic fluid from holography
• Optomechanical Response of a Strongly Interacting Fermi Gas
• Bulk viscosity of dual Bose and Fermi gases in one dimension
• Spin conductivity spectrum and spin superfluidity in a binary Bose mixture
• Large-momentun tail of one-dimensional Fermi gases with spin-orbit coupling
• Dissipative superfluid hydrodynamics for the unitary Fermi gas