Title: Derivation of a Non-autonomous Linear Boltzmann Equation from a Heterogeneous Rayleigh Gas,
Abstract: A linear Boltzmann equation with nonautonomous collision operator is
rigorously derived in the Boltzmann-Grad limit for the deterministic dynamics
of a Rayleigh gas where a tagged particle is undergoing hard-sphere collisions
with heterogeneously distributed background particles, which do not interact
among each other. The validity of the linear Boltzmann equation holds for
arbitrary long times under moderate assumptions on spatial continuity and
higher moments of the initial distributions of the tagged particle and the
heterogeneous, non-equilibrium distribution of the background. The empiric
particle dynamics are compared to the Boltzmann dynamics using evolution
semigroups for Kolmogorov equations of associated probability measures on
collision histories.