Collective Motion in Simple Classical Fluids

Abstract

An earlier study of variational solutions of the Liouville equation for simple fluids is extended to include high-frequency thermal excitations. In the long-wavelength limit, variational eigenvalues are determined in correspondence with dispersion relations derived from linearized Navier-Stokes equations which contain frequency-dependent viscous and thermal transport coefficients. Two distinct sets of high-frequency longitudinal excitations arise. In the limit that mechanical moduli are much larger than thermal moduli, one of these excitations simplifies to a quasiphonon composed only of velocity fluctuations and associated time derivatives. On the other hand, in the case of vanishing viscosity, the excitation is seen to be composed only of energy fluctuations and time derivatives of energy fluctuations and, as such, may be the classical analog of high-frequency second sound in liquid He II. The various eigenfunctions are discussed in relation to results of recent neutron-scattering experiments.