Approximate Eigenfunctions of the Liouville Operator in Classical ManyBody Systems
Abstract
A variational criterion is used to find approximate eigenfunctions and eigenvalues of the Liouville operator in classical manybody systems. The trial functions are taken to be sums over molecules of functions depending on the position and momentum of a single molecule. In a harmonic lattice, this approach leads to exact eigenfunctions and eigenvalues. In a fluid, the eigenvalue spectrum is continuous, and the eigenfunctions are related to those found by Van Kampen in his study of the linearized Vlasov equation for a plasma. The time dependence of the fluid current density is found by means of these eigenfunctions and eigenvalues. The results show persistent freeparticle propagation and damped soundwave propagation, with relative importance depending on the magnitude of the sound velocity.
 Publication:

Physical Review
 Pub Date:
 April 1966
 DOI:
 10.1103/PhysRev.144.170
 Bibcode:
 1966PhRv..144..170Z