Long-time tail in velocity correlations in a one-dimensional Rayleigh gas

The markovian Boltzmann equation for a newtonian gas consisting of two kinds of particles (test and host species) is evaluated analytically by means of systematic scaling methods for the one-dimensional system in the Rayleigh limit of heavy test particles. In the spatially uniform situation the velocity autocorrelation function of the test particles obeys a remarkably simple differential-integral equation. Elementary Laplace analysis reveals an exact t^-3 long-time tail.