Approximate Eigenfunctions of the Liouville Operator in Classical Many-Body Systems. II. Hydrodynamic Variables

Abstract

A variational solution of the Liouville equation is used to obtain collective coordinates for simple classical fluids. Comparison is made with macroscopic analogs determined from relevant hydrodynamic equations. Approximate eigenfunctions of the Liouville operator, when constructed from linear combinations of the spatial Fourier transforms (fluctuations) of the mass, momentum, and energy-density operators for the fluid, are found appropriate to low-frequency disturbances. When time derivatives of fluctuations are included among trial functions, the variational procedure provides fluid-state counterparts of usual solidstate phonons.