Boltzmann equation and hydrodynamic fluctuations

TL;DR

This paper derives generalized hydrodynamics equations from the linearized Boltzmann equation using invariant manifolds, calculates exact transport coefficients, and compares theoretical predictions with experimental data for density fluctuations.

Contribution

It introduces a novel application of invariant manifolds to derive hydrodynamic equations and compute transport coefficients from the Boltzmann equation.

Findings

Exact transport coefficients obey Green-Kubo formulas

Spectrum of density fluctuations matches experimental data

Hydrodynamics valid at finite Knudsen numbers and frequencies

Abstract

We apply the method of invariant manifolds to derive equations of generalized hydrodynamics from the linearized Boltzmann equation and determine exact transport coefficients, obeying Green-Kubo formulas. Numerical calculations are performed in the special case of Maxwell molecules. We investigate, through the comparison with experimental data and former approaches, the spectrum of density fluctuations and address the regime of finite Knudsen numbers and finite frequencies hydrodynamics.