Transport coefficients from the Boson Uehling-Uhlenbeck Equation

TL;DR

This paper derives microscopic expressions for transport coefficients of a quantum Bose gas above the critical temperature, using a novel perturbation approach linked to the collision operator eigenvalues, and provides numerical results for shear viscosity and thermal conductivity.

Contribution

It introduces a perturbation method based on Rayleigh-Schrodinger theory to compute transport coefficients of a Bose gas, improving accuracy over traditional methods.

Findings

Bulk viscosity remains zero, as in classical gases.

Numerical values for shear viscosity and thermal conductivity are provided.

The approach links transport coefficients to collision operator eigenvalues.

Abstract

We derive microscopic expressions for the bulk viscosity, shear viscosity and thermal conductivity of a quantum degenerate Bose gas above $T_C$, the critical temperature for Bose-Einstein condensation. The gas interacts via a contact potential and is described by the Uehling-Uhlenbeck equation. To derive the transport coefficients, we use Rayleigh-Schrodinger perturbation theory rather than the Chapman-Enskog approach. This approach illuminates the link between transport coefficients and eigenvalues of the collision operator. We find that a method of summing the second order contributions using the fact that the relaxation rates have a known limit improves the accuracy of the computations. We numerically compute the shear viscosity and thermal conductivity for any boson gas that interacts via a contact potential. We find that the bulk viscosity remains identically zero as it is for the classical case.