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

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 τ<Subscript>0</Subscript>, t ≫τ<Subscript>0</Subscript>, 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 <InlineEquation ID="Equ1"> <EquationSource Format="TEX">$n^{-1}(\partial / \partial \mathaccent"017E{r}) n$</EquationSource> </InlineEquation> are small. It relates the hydrodynamic form of the one-particle distribution function to spectral properties of operators involved in linear Boltzmann equation. Copyright EDP Sciences/Società Italiana di Fisica/Springer-Verlag 2006