Microscopic derivation of the Boltzmann equation for transport coefficients of resonating fermions at high temperature

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.

12 pages, 7 figures; (v2) numerical results in Sec$.$IV corrected; (v3) published version

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• Many-Body Physics with Ultracold Gases
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• Theory of ultracold Fermi gases
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• Nonrelativistic conformal field theories
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Cited by in corpus (6)

• Transport in p-wave interacting Fermi gases
• Thermal conductivity of a weakly interacting Bose gas in quasi-one-dimension
• Bulk viscosity of resonantly interacting fermions in the quantum virial expansion
• Viscous Flow in a 1D Spin-Polarized Fermi Gas: the Role of Integrability on Viscosity
• Exact perturbative expansion of the transport coefficients of a normal low-temperature Fermi gas with contact interactions
• Viscous Drude weight of dual Bose and Fermi gases in one dimension