Eur. Phys. J. B 53, 225-232 (2006)
https://doi.org/10.1140/epjb/e2006-00369-4

Linear kinetic equation: long-time behavior of one-particle distribution function

¹ Institute of Physics, P.O. Box 68, Belgrade, 11080, Serbia and Montenegro
² Faculty of Engineering, Trg D. Obradovića 6, Novi Sad, 21000, Serbia and Montenegro

Corresponding author: ^a vrhovac@phy.bg.ac.yu

Received: 29 June 2006
Revised: 31 August 2006
Published online: 13 October 2006

Abstract

We construct asymptotic (long-time) solution of the linear Boltzmann equation using the time-dependent perturbation theory generalized to non-Hermitian operators. We prove that for times much larger than the relaxation time τ₀, t ≫τ₀, one-particle distribution function separates into spatio-temporal and velocity dependent parts, and provide the explicit expression for the long-time solution of the linear Boltzmann equation. Our analysis does not assume that relative density gradients are small. It relates the hydrodynamic form of the one-particle distribution function to spectral properties of operators involved in linear Boltzmann equation.