The crossover from classical to quantum transport in a weakly-interacting Fermi gas

TL;DR

This paper provides an exact solution to the quantum kinetic equation for a weakly interacting Fermi gas, bridging the gap between quantum and classical transport regimes with improved accuracy over traditional approximations.

Contribution

It introduces a novel polynomial-based method for solving the quantum kinetic equation, enabling precise predictions of transport properties across regimes.

Findings

Accurate predictions of shear viscosity, thermal diffusivity, and spin diffusivity.

Relaxation-time approximation fails significantly at low temperatures.

Method offers efficient benchmarking for strongly correlated quantum gases.

Abstract

We present an exact solution of the quantum kinetic equation of a weakly interacting Fermi gas in the crossover from the degenerate Fermi-liquid regime to the classical Boltzmann gas. We construct families of orthogonal polynomials tailored to each angular momentum channel, enabling a fast and systematically improvable decomposition of the phase-space distribution. This approach yields accurate, non-variational predictions for the shear viscosity, thermal diffusivity, and spin diffusivity to leading order in the scattering length. We demonstrate that the commonly used relaxation-time approximation fails dramatically at low temperature--by up to 25%. Our method provides a numerically efficient framework for benchmarking transport in strongly correlated regimes and for simulating the kinetics of quantum gases beyond hydrodynamics.