Lagrange theory of thermal hydrodynamic fluctuations and collective diffusion in liquids

The basis of the Lagrange theory of the thermal hydrodynamic fluctuations in liquids is constructed. The behaviour of the velocity autocorrelation function and mean-square displacement of the Lagrange particle are considered in detail. The application of the obtained results to the molecular dynamic problems is discussed. An analysis of collective contributions to the self-diffusion process in simple liquids is given