Diffusion and velocity relaxation of a Brownian particle immersed in a viscous compressible fluid confined between two parallel plane walls

The diffusion tensor and velocity correlation function of a Brownian particle immersed in a viscous compressible fluid confined between two parallel plane walls are calculated in point approximation. The fluid is assumed to satisfy stick boundary conditions at the walls. It is found that the velocity correlation function decays asymptotically with a negative t(-2) long-time tail due to coupling to overdamped sound waves. The coefficient of the long-time tail is calculated and shown to be independent of fluid viscosity.