Microscopic derivation of the Boltzmann equation for transport coefficients of resonating fermions at high temperature
arXiv:2103.10123 · doi:10.1103/PhysRevA.103.053320
Abstract
Motivated by the recently observed failure of the kinetic theory for the bulk viscosity, we in turn revisit the shear viscosity and the thermal conductivity of two-component fermions with a zero-range interaction both in two and three dimensions. In particular, we show that their Kubo formula evaluated exactly in the high-temperature limit to the lowest order in fugacity is reduced to the linearized Boltzmann equation. Previously, such a microscopic derivation of the latter was achieved only incompletely corresponding to the relaxation-time approximation. Here, we complete it by resuming all contributions that are naively higher orders in fugacity but become comparable in the zero-frequency limit due to the pinch singularity, leading to a self-consistent equation for a vertex function identical to the linearized Boltzmann equation. We then compute the shear viscosity and the thermal conductivity in the high-temperature limit for an arbitrary scattering length and find that the Prandtl number exhibits a nonmonotonic behavior slightly below the constant value in the relaxation-time approximation.
arXiv comment12 pages, 7 figures; (v2) numerical results in SecIV corrected; (v3) published version
References in corpus (35)
- Many-Body Physics with Ultracold Gases
- Viscosity in Strongly Interacting Quantum Field Theories from Black Hole Physics
- Theory of ultracold Fermi gases
- Hydrodynamic Transport Coefficients in Relativistic Scalar Field Theory
- From Quantum Field Theory to Hydrodynamics: Transport Coefficients and Effective Kinetic Theory
- General coordinate invariance and conformal invariance in nonrelativistic physics: Unitary Fermi gas
- Nonrelativistic conformal field theories
- Universal Quantum Viscosity in a Unitary Fermi Gas
- BCS-BEC Crossover and the Unitary Fermi Gas
- Viscosity and scale invariance in the unitary Fermi gas
- Scale invariance and viscosity of a two-dimensional Fermi gas
- Vanishing bulk viscosities and conformal invariance of unitary Fermi gas
- Conformal Invariance for Non-Relativistic Field Theory
- Viscous relaxation and collective oscillations in a trapped Fermi gas near the unitarity limit
- 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
- Universal Sound Diffusion in a Strongly Interacting Fermi Gas
- Shear viscosity of a universal Fermi gas near the superfluid phase transition
- Observation of conformal symmetry breaking and scale invariance in expanding Fermi gases
- Virial expansion with Feynman diagrams
- Anomalous minimum in the shear viscosity of a Fermi gas
- Thermal Conductivity and Sound Attenuation in Dilute Atomic Fermi Gases
- Scale breaking and fluid dynamics in a dilute two-dimensional Fermi gas
- Searching for Perfect Fluids: Quantum Viscosity in a Universal Fermi Gas
- High-temperature expansion of the viscosity in interacting quantum gases
- Bulk viscosity and contact correlations in attractive Fermi gases
- Hydrodynamic tails and a fluctuation bound on the bulk viscosity
- Viscosity spectral functions of resonating fermions in the quantum virial expansion
- Shear viscosity and spin diffusion coefficient of a two-dimensional Fermi gas
- Shear viscosity and damping of collective modes in a two-dimensional Fermi gas
- Measuring the Hydrodynamic Linear Response of a Unitary Fermi Gas
- Renormalized Linear Kinetic Theory as Derived from Quantum Field Theory - a novel diagrammatic method for computing transport coefficients -
- Hydrodynamics with spacetime-dependent scattering length
- Quantum critical thermal transport in the unitary Fermi gas
- Bulk viscosity of resonating fermions revisited: Kubo formula, sum rule, and the dimer and high-temperature limits
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- Viscous Drude weight of dual Bose and Fermi gases in one dimension