Excitation and damping of zero sound in classical liquids: A new memory function approach

Collisions between atoms through the intermediary of zero sound wave of finite lifetimes are discussed to account for the memory effect on the density correlations of atoms. The second-quantization formalism is used to describe the formation and decay of zero sound, and a new non-markovian kinetic equation is derived. It is shown that the memory term is of the same form as that in the usual approach based on the Mori formalism, but arises from the finite duration of the above-mentioned collision process. The Fokker-Planck-type term, which is non-markovian in the usual approach, is shown to be markovian, describing the instantaneous change of velocity due to emission or absorption of zero sound. A short-time approximation is made to calculate the dispersion relation of zero sound. The lifetimes are found to be of order 10-12s, which is consistent with the observed Brillouin side peaks.