Propagation of Disturbances at High Frequencies in Gases, Liquids, and Plasmas

A method is developed for investigating the propagation of disturbances at small amplitude in fluids from the molecular or ionic standpoint. Adopting as variables the displacements of the particles from a configuration of thermal equilibrium, the equations of motion are derived, in statistical form, for both classical and quantum mechanics. It is shown how to apply this theory in the high-frequency region by neglecting the correlation between the displacements of neighboring particles. Relaxation frequencies are defined, and it is shown that anomalous absorption and dispersion will be found in their neighborhood. Beyond the relaxation frequency, the medium will show elastic or dispersive properties, according to whether the thermal velocities are below or exceed the velocity of propagation. A completely ionized system will have no relaxation frequencies.