On the Attenuation of Sound in Liquid Helium

Abstract

In terms of a two-particle Green function, we formulated the three-phonon process. The spectral function of the Green function is the dynamical structure factor of liquid and there are two exact sum rules for it. Using Puff’s expression for the dynamical structure factor, it is shown that one can reproduce results obtained by Pethick and ter Haar who formulated the three-phonon process in terms of a single-particle function. In the framework of this theory we can put problems in connection with the fluctuation-dissipation theorem. A sum rule for the width Γ(k, ω), which is expressed as the time Fourier transform of the time correlation function of the random force acting upon the density fluctuation, is obtained. As long as k²Γ<<k_BT, the liquid structure factor S(k) is given by
(Remark: Graphics omitted.).
The connection between the width Γ(k, ω) and the lifetime of phonons is discussed. Properties of the random force are also discussed.