Mesoscopic dynamics of fermionic cold atoms ---Quantitative analysis of transport coefficients and relaxation times---

TL;DR

This paper provides a detailed quantitative analysis of transport coefficients and relaxation times in fermionic cold atomic gases using a microscopic RG approach, highlighting quantum effects and temperature dependencies.

Contribution

It introduces a novel microscopic method based on the RG approach to accurately compute hydrodynamic properties without relying on ansatzes.

Findings

The relation τ_π = η/P holds well in the studied systems.

The relation for viscous relaxation time τ_J is only approximately valid.

Quantum statistical effects significantly influence transport coefficients.

Abstract

We give a quantitative analysis of the dynamical properties of fermionic cold atomic gases in normal phase, such as the shear viscosity, heat conductivity, and viscous relaxation times, using the novel microscopic expressions derived by the renormalization group (RG) method, where the Boltzmann equation is faithfully solved to extract the hydrodynamics without recourse to any ansatz. In particular, we examine the quantum statistical effects, temperature dependence, and scattering-length dependence of the transport coefficients and the viscous relaxation times. The numerical calculation shows that the relation $\tau_\pi=\eta/P$, which is derived in the relaxation-time approximation (RTA) and is used in most of the literature, turns out to be satisfied quite well, while the similar relation for the viscous relaxation time $\tau_J$ of the heat conductivity is satisfied only approximately with a considerable error.