On the theory of Brownian motion in compressible fluids

Within the framework of the theory of hydrodynamic fluctuations the Brownian motion of a spherical particle in a compressible fluid has been considered taking into account the action of a harmonic potential. The general relations for the velocity autocorrelation function and mean square displacement of a Brownian particle have been established by means of the solutions of the generalized Langevin equation. The analysis for the time evolution of the correlations has been performed both on large and small time scales. On a large time scale the asymptotic expansions describing the persistent correlations have been found to arbitrary order in . The transition to the system without potential has been studied and the conditions for realization of the diffusion regime of correlations have been clarified. On a small time scale a consistent limit procedure for the velocity autocorrelation function has been used which leads in a straightforward manner to the well-known result given by the equipartition theorem.