Boltzmann equation and hydrodynamic fluctuations

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.

This is a more detailed version of a related paper: I.V. Karlin, M. Colangeli, M. Kroger, PRL 100 (2008) 214503, arXiv:0801.2932. It contains comparison between predictions and experiment, in particular. 11 pages, 6 figures, 2 tables

References in corpus (4)

• Boltzmann equations for mixtures of Maxwell gases: exact solutions and power like tails
• Exact linear hydrodynamics from the Boltzmann equation
• From hyperbolic regularization to exact hydrodynamics for linearized Grad's equations
• Hyperbolicity of exact hydrodynamics for three-dimensional linearized Grad's equations

Cited by in corpus (11)

• Entropic 13 Moment Equations from Boltzmann's Kinetic Equation
• Fluctuation-dissipation relation for chaotic non-Hamiltonian systems
• Molecular hydrodynamic theory of the velocity autocorrelation function
• Trapping in bottlenecks: interplay between microscopic dynamics and large scale effects
• Current in a quantum driven thermostatted system with off-diagonal disorder
• Fluctuations in quantum one-dimensional thermostatted systems with off-diagonal disorder
• A reduction scheme for coupled Brownian harmonic oscillators
• Reduced Markovian Descriptions of Brownian Dynamics: Toward an Exact Theory
• Model reduction of Brownian oscillators: quantification of errors and long-time behaviour
• Towards a quantitative reduction of the SIR epidemiological model
• Nonequilibrium Response from the dissipative Liouville Equation