Collective Motion of Particles at Finite Temperatures

Abstract

A quantum-statistical theory of frequency spectra and damping constants of the col­ lective motion of interacting particles at finite temperatures is presented, and used to clarify several problems. The formulation is based on the explicit recognition of the fact that a set of collective variables , properly chosen describe the collective motion in such a way that the average values of the collective variables at a time determine their average values thereafter. The frequency distribution of the density fluctuations in fluids is thus analyzed, and molecular expressions for the intensities and widths of the spectral lines are obtained. The widths are written in terms of generalized transport coefficients which depend upon the wavelength of the collective oscillation or the frequency spectrum. The expressions are valid even in the case in which the hydrodynamical description is inapplicable, and turn out to be useful for describing the sound attenuation in liquid helium II at low temperatures and the inelastic scattering of neutrons by liquids. The transport coefficients of fluids are formulated in terms of equilibrium fluctuations from a new point of view without the use of the local equilibrium ensemble. The results for the shear viscosity and thermal conductivity agree with those obtained by the author previously. A new term, however, is found to be added to the dynamical flux determining the bulk viscosity. This term arises as a result of subtracting a pressure fluctuation as­ sociated with the fluctuation of the mass and energy densities to define a random force.